Wednesday, December 19, 2018

The relation between life changes, stress, and illness

I have often wondered about my personal experience and the anecdotal evidence that when you get stressed you seem more likely to get a cold or the flu. I finally found some research literature on the subject.
A helpful review is
Modern Approaches to Conceptualizing and Measuring Human Life Stress
Scott M. Monroe

A seminal paper from 50 years ago
The social readjustment rating scale 
TH Holmes, RH Rahe

The authors developed a quiz to estimate how your recent life circumstances and changes may be producing different levels of stress. They then correlated the stressful life circumstances to recent illness of the subjects.

It is worth occasionally doing the quiz. Here is one version.
Aside: One interesting aspect is that positive changes can create stress (e.g. starting a new job, getting married, having a baby, ...).

However, as discussed in detail by Monroe in his review all of this is more complicated than we might like. Measures of stress are subjective, subtle, personal, and hard to agree upon. For example, do you define the level of stress largely in terms of the environment or in terms of the response of the individual to the environment?
This is hardly surprising given that the subject is at the interface of medicine, psychology, and sociology.

Saturday, December 15, 2018

Metastability and first-order phase transitions

One of the simplest examples of a first-order phase transition is occurs in a ferromagnet at a temperature below the critical temperature and in an external magnetic field. The transition occurs when the field is varied so that it changes sign.

This can be described in terms of the following Landau free energy where H is the external field and r is negative.
One observes hysteresis as for non-zero H there is a metastable state.
The order parameter phi versus H is shown below

The boundaries of the region of metastability are defined by the field Hc given by
The above description is taken from a review article by Kurt Binder.
I have never seen this in a textbook.
Have you?
Any clear detailed presentations of this topic would be appreciated.

Monday, December 3, 2018

What should everyone know about science?

In a time when misunderstandings of science anti-science views are rising around the world, it is important that scientists do a better job of communicating to the broader public what science actually is, what it can do, and what it cannot do.

An interesting and important question is what it is that people should know and understand. There is a multitude of views on this (which is not necessarily a completely bad thing).

I only learned last week that in 1994, Phil Anderson had tackled this issue in a short article he wrote for The Daily Telegraph, a London-based newspaper. An interesting paper about Anderson's article just appeared. It nicely places the article in a broader context and gives a more recent perspective on the issues he raised.

Four Facts Everyone Ought to Know about Science:
The Two-Culture Concerns of Philip W. Anderson
Andrew Zhang and Andrew Zangwill

The four ``facts'' that Anderson chose were (as paraphrased by Zhang and Zangwill):

1. Science is not democratic.
2. Computers will not replace scientists.
3. Statistical methods are misused and often misunderstood.
4. Good science has aesthetic qualities.

This is a fascinating choice. 

One thing I learned was about Anderson's argument that Bayesian methods should have been used to rule out the significance of "discoveries" such as the 10 keV neutrino and the fifth force. In 1992 he wrote a Physics Today column on the subject.

Monday, November 26, 2018

A case for (and against) multi-dimensional measures

I am a vocal critic of the use of metrics to evaluate individuals, single scientific papers, journals, sub-fields, institutions, ....
However, my problem is really one of abuse. I don't think metrics are totally meaningless or useless. Rather, it is the mindless use of metrics, with a disregard for their limitations, that is a problem.

This post is not about metrics, jobs, and funding. I have probably already written too many posts on that. Rather, I want to give two examples where I have found some multi-dimensional metrics helpful, when considering issues relating to public policy and development, particularly in the Majority World.

The case is that of the HDI (Human Development Index). Prior to its introduction people tended to use GDP (Gross Domestic Product) as a measure of how a country was performing and where it ranked in the world. In contrast, the HDI is a composite metric, factoring in income per capita, life expectancy, and education. The map below gives a sense of how the HDI varies around the world.

There is a lot one can learn from just the map.  Sub-saharan Africa is the worst as a region. Even though India now has a middle class of several hundred million people, it is still comparable to some African countries.

Whenever I need to know something about a country, I look at the HDI. The fact that Australia often ranks in the top 3 tells me what a privileged environment I live in. Unfortunately, too many Australians really don't know or appreciate this.

I recently met a medical doctor from Niger [which I knew nothing about it]. He told me that Niger is ranked 182 out of 182 countries! This quickly gave me a sense of some of the challenges he faces.

Obviously, like any metric it has limitations. For example, some people prefer the IHDI (Inequality-adjusted HDI). The USA ranks 25th on the HDI.

The second example of a multi-dimensional metric concerns broader issues than human development, that is "human flourishing". This often means quite different things to different people. Last year there was a nice paper in PNAS that argues why this is important for both public policy, but also research in medicine and social sciences.

On the promotion of human flourishing 
Tyler J. VanderWeele

The abstract gives an excellent summary.
Many empirical studies throughout the social and biomedical sciences focus only on very narrow outcomes such as income, or a single specific disease state, or a measure of positive effect. Human well-being or flourishing, however, consists in a much broader range of states and outcomes, certainly including mental and physical health, but also encompassing happiness and life satisfaction, meaning and purpose, character and virtue, and close social relationships. The empirical literature from longitudinal, experimental, and quasi-experimental studies is reviewed in an attempt to identify major determinants of human flourishing, broadly conceived. Measures of human flourishing are proposed. Discussion is given to the implications of a broader conception of human flourishing, and of the research reviewed, for policy, and for future research in the biomedical and social sciences.
Broadly, when trying to describe and understand complex systems one should search for some measures of the properties of the system. Given the systems are complex one may need several measures. These will never be complete or perfect. But, provided one uses them with the appropriate caution this is a good thing.

Monday, November 19, 2018

How much background material do beginning graduate students need to master?

I am working with a graduate student beginning research and she has asked this important question. I don't think there is a simple universal answer.

Background material includes review articles of a field, details of an experimental technique or computer code, details of derivations, seminal articles on the topic, ....

At the UQ condensed matter theory group meeting, we had a brief discussion about the question.
Answers from students, both beginning and advanced, were helpful. It also underscored how important the question is because students really do struggle with this issue. One shared how he developed some mental health problems because at the beginning of his Ph.D. he was too obsessive about understanding all the details. The question and discussion underscored to me how we need to have more discussions of this nature.

Beginning research is a difficult transition for most graduate students. When they were undergraduates they often could understand all the details and work through all the derivations.
(They are unlike a significant fraction of undergraduates who just don't seem to realise that the details DO matter.)
However, the painful reality is that what was possible for a gifted and motivated undergraduate is simply not possible for most Ph.D. research.
Research fields are so vast and have so much foundational material a student simply does not have the time to check everything and understand everything in full.
The question is painfully relevant in Australia because Ph.D. students do not do coursework (or a Masters degree) and the government continues to reduce the number of years of funding.
Furthermore, the "publish or perish" culture puts pressure on students and advisors to be cranking out papers, which means there is pressure for students not to ``waste time'' on slow and deep learning of background material.

Like many things in life, I think answers to the question require some balance and need to allow for differences in personality, learning styles, personal goals, and nature of the research topic.

Here are some composite pictures to illustrate the extremes and the associated problems and potential.

Sanjay loves to understand and master details. He is also interested in the big foundational questions the research might address. When he reads an article he likes to work through all the details of the mathematical derivations. He would prefer to write his own computer code so he really knows what is going on. He has a large stack of papers on his desk, waiting to be read, consisting of many of the papers related to his research topic. After a year he is still learning background material. However, in his third year, he has a big breakthrough because he realises that one a key assumption/derivation in the field is wrong in certain cases. He not only corrects it but opens up a new avenue of research.

Priya just wants to get on with research and is not a detail oriented person. Following her advisors request she reads a few background articles superficially and dives into research. However, she does not really grasp the big picture or understand the limitations of the technique she is using. Consequently, she wastes a lot of time making mistakes, producing dubious results, and getting help for things she should have worked out for herself. However, this approach actually suits her learning style and she does eventually learn the essential things she needs to know and understand what is going on. Furthermore, because she has "dived in'' early, by the end of her Ph.D. she has produced several nice papers.

What do you think?
It would be good to hear from beginning graduate students, advanced graduate students, and faculty advisors.
What did you do? What do you wish you had done?

Monday, November 12, 2018

Universality, probability, and the growth of rough surfaces

On Friday there was a nice UQ Maths and Physics Colloquium, Beyond the Gaussian Universality Class, given by Ivan Corwin,
The talk was a very nice example of synergy between fundamental physics and maths research.
There are interesting connections with simple one-dimensional models for surface growth, the Kardan-Parisi-Zhang equation, the KPZ universality class, traffic models, random matrix theory, directed polymers in random media, ....

Friday, November 9, 2018

Some hypotheses about universities

In the next month, I have been asked to give a talk and to write an article about universities in two different forums. What are universities for? How do they promote human flourishing?

Before I get too carried away I thought I would float a few ideas/claims/hypotheses that will be central to my argument that there needs to be a greater debate about fundamental issues and about the history of universities.

Some of the claims are interconnected.
In future posts, I may expand on some of these claims.

Universities are currently having a crisis of identity, mission, and purpose.

This crisis arises because there is a multitude of competing and conflicting visions from a range of "stakeholders".

This crisis and the degree of conflict is far greater and deeper than those faced by other institutions: government, schools, hospitals, business, charities, ...

Over time universities have been one of the most successful human institutions for promoting human flourishing (broadly defined) in many different ways: training leaders, science that produces useful technology, enriching cultural life, ...

Universities are a victim of their success.
Their current struggles follow the natural evolution of successful and growing organisations. 
Success increases the size, complexity, and cost of the organisation. Success also attracts "hangers on" who want a piece of the action: money, power, and social status. They do not have the same vision as the founders and first few generations of builders of the organisation. Their focus is more on their own agenda and interests than on the "common good" that the organisation originally sought to serve. This is a large part of the origin of the competing and conflicting visions.
Success also leads to the iron triangle of cost, access, and quality.

Here I expand on the first few claims.

Universities are currently having a crisis of identity, mission, and purpose.
I have written about this before. I think it is nicely illustrated by the diverse voices that claim this.

Universities on the Defensive 
Hunter Rawlings, a former President of Cornell, and currently the President of the Association of American Universities, a consortium of 60 of the leading North American universities.

The Slow Death of the University
Terry Eagleton, a distinguished literary critic, former Oxford Professor, and Marxist.

Higher Education is Drowning in BS,
by Christian Smith, a sociologist at the University of Notre Dame.

The crisis is not just about research universities in Western countries but also smaller teaching institutions and large state universities in the Majority World. Last year I was involved in a range of consultations run by a global NGO, identifying big issues in universities, and it was surprising how often this question, ``What is a university for?" came up.

This crisis arises because there is a multitude of competing and conflicting visions from a diverse range of "stakeholders".
The latter includes faculty, administrators, students, parents, alumni, future employers, politicians, taxpayers, funding agencies, donors, ...
The conflicting visions include neoliberalism, job training, a finishing school for the privileged, nation building, sectarian religious, social critique, scholarship, social transformation....

This crisis and the degree of conflict is far greater and deeper than those faced by other institutions.
One might argue that many public institutions (government, schools, hospitals, business, charities, ...) are currently in turmoil. However, most of these conflicts are about funding, governance, internal codes of conduct, and how to respond to rapid social and technological change. They are not conflicts about the primary purpose of the institution. One might also claim that as societies have become more multi-cultural, more politically divided, and complex this crisis just reflects, the many competing voices in the public square at large.
However, I would contend that universities are one of the most contested public institutions in society today. There are comparable debates about funding and access to health care. However, everyone agrees on the mission of hospitals: to help cure sick people. There is little debate about the goal, about the methodologies, or about the relative importance of different sub-fields of medicine. In contrast, in universities, there is significant contention about what the actual primary mission is and of the relative importance of different academic disciplines. No one proposes a large hospital without a pathology or oncology department. However, there are people who think humanities now have little to contribute to universities.

What do you think?
Which of my claims do you disagree with?

Monday, November 5, 2018

Bad metallic behaviour in ultracold atoms

There is a nice paper
Bad metallic transport in a cold atom Fermi-Hubbard system 
Peter T. Brown, Debayan Mitra, Elmer Guardado-Sanchez, Reza Nourafkan, Alexis Reymbaut, Simon Bergeron, A.-M. S. Tremblay, Jure Kokalj, David A. Huse, Peter Schaus, and Waseem S. Bakr

The paper represents a significant experimental advance in using ultracold atoms to investigate questions directly relevant to strongly correlated electron systems. In this case, the system Hamiltonian can be tuned to be a Hubbard model on a square lattice, such that the model parameters, U and t, and the doping, n are known.
One limitation is that current experiments can only be performed down to the lowest temperature of T/t =0.3. [For comparison, for cuprates this is of the order of 1000 K!].
Using imaging techniques the authors are able to directly extract the density (charge) diffusion constant D and the density susceptibility, chi, shown below. The experimental data are red dots. The blue curve is the result of calculations based on the Finite Temperature Lanczos Method (FTLM). Green dots the results of Dynamical Mean-Field theory. Gamma is the density relaxation rate.

Both the experiment and the ability to make such a detailed comparison with concrete theoretical calculations is a significant and exciting achievement.

The dashed curve in the upper panel is the value of the diffusion constant associated with the Mott-Ioffe-Regel limit below which one expects bad metal behaviour.
Aside: one should always keep in mind that for the MIR limit, different authors use different criteria, leading to different factors of pi, sqrt(pi), ...

Using the Nernst relation, sigma = chi * D,  the data above gives the conductivity (sigma) and resistivity (rho), shown below.
The blue and green curves correspond to the predictions, of FTLM and DMFT, respectively. The dashed grey line is the Mott-Ioffe-Regel limit.

One comment I have concerns an additional comparison that the authors could make. Based on heuristic arguments and results from AdS-CFT, Hartnoll conjectured a lower bound for the diffusion constant, hv_F^2/T.
Previously, Nandan Pakhira and I showed that this bound was significantly violated in the bad metallic regime, as described by DMFT.

There is also a commentary on the paper by Ehud Altman at the Journal Club of Condensed Matter.
I thank Matt Davis for bringing the paper to my attention.

Wednesday, October 31, 2018

Some basic ideas about teaching

Over the past few decades, I have taught a wide range of courses in diverse contexts. Perhaps I have been slow to learn how to be a better teacher. Since I began teaching things have changed dramatically. Our goals and the content of most curricula have changed little, and should not. However, advances in technology provide new opportunities but also challenges and potential distractions. The social context has changed significantly in terms of the expectations of both students and institutions.

Here are a few of the ideas that I think are important to keep in mind.  Some seem obvious, particularly in hindsight. On the other hand, practical implementations are a challenge. I think keeping the ideas in mind is also important for maintaining your sanity and motivation.
The ideas are listed in no particular order and many are interconnected.

The amount of learning that happens is correlated with the level of student engagement.
Engagement happens at many levels and in many ways: through attendance, listening carefully, taking notes, asking questions, reading texts, talking to classmates about content, working on problems, watching relevant videos, thinking about content, ...
Consequently, a good teacher explores strategies to increase student engagement. However, there is a limit to what you can do. This is why I despair of the situation in most beginning undergraduate classes in Australia. For example, in the last course that I taught there were about 100 students enrolled. Only about 30 actually showed up for class, and only about 20 used clickers in class to engage. Videos of the lectures are available (because of mandatory university policy), increasing the temptation of students to not attend. But most videos have viewed a handful of times. This is quite representative. It sadly contrasts to some different contexts I have taught where there is a very high level of student engagement.

The curriculum should be your servant not your master.
Textbooks get thicker and thicker with time. More and more content gets crammed into curricula. This increases the pressure to "cover material", even if students learn little. I recently had the opportunity to teach a whole course and took the liberty to reduce content and focus on depth of understanding. I think the outcomes were much better.

Accept and work with the hand of cards you that have been dealt.
We all have fantasies of teaching a class with students that are all gifted, well prepared, highly engaged, highly motivated, and appreciative. However, it never happens! We need to accept who they are, where they are at and adapt our expectations, strategies and academic level.

Flip, blend and mix the classroom.
On the one hand, there is a lot of hype about the value of "flipping the classroom",  online courses, and peer instruction. On the other hand, I am told (and I have my own anecdotal experience) that there is significant research that does show that a "blended" class [i.e. a combination of online and face-to-face] instruction is effective. I find that regular online quizzes and reflections do increase student engagement and give me helpful feedback about learning progress. But, expect some student resistance and complaints. If you reduce traditional lecturing a few students will complain that you aren't "teaching them" or that they are ``not getting their money's worth''!
Different students have different learning styles. Furthermore, today's students are more video oriented than text-oriented and have shorter attention spans. Hence, in a single class hour, there is value in a mixture of traditional lecture, short video clips, small group discussion, ...

Be mindful of the undercurrent of complex social and psychological dynamics in the classroom.
Students are human! They come to class with a lot of emotional and intellectual "baggage",  both good and bad: aspirations, gifts, expectations, insecurities, prejudices, excitement, preconceived ideas, fears, hopes, ...
Furthermore, they are not just individuals but a social unit. Your students have a relationship with you and with one another: positive, negative, ambivalent, or non-existent.
All this complex dynamics has the potential to enhance or to hinder learning. Unfortunately, much of it we have no control over. On the other hand, if we can discern some of the dynamics and respond appropriately it can enhance learning significantly.

Learning is enhanced through personal relationships.
Even extreme introverts are wired to be relational and yearn for meaningful relationships. They just want a few select relationships.

Accept that you will never make everyone happy.
It never ceases to amaze me how polarised student feedback and teaching evaluations are. You are the best/worst teacher they have ever had. This is the best/worse course they have taken. The course is too hard/easy... This is all for the same course and teacher! Don't take the feedback so personally.

What do you think?
Any other things that you think are important.

Wednesday, October 24, 2018

Advice for beginning bloggers

A friend asked me for any advice I have before he launches a blog. What mistakes have I made? How do I manage comments? What is the best platform?
So here are my rough thoughts.

Just do it!
This applies to both starting, persevering, and what you write. Blogging is not for perfectionists and procrastinators. A major strength (and weakness) of the medium is that one can float tentative and controversial ideas and not worry about endless editing and polishing. It can be an incredibly enriching experience, for both yourself and others.

The biggest impact of your blog may be on you not on your audience.
This is really true in my case. Blogging has clarified my thinking on a wide range of issues, from science to politics to religion.

Blogging saves time rather than taking time.

Don't be driven by metrics.
It is easy to keep track of page views and an abundance of other data. It is not clear how accurate or helpful it is. Furthermore, this can easily lead to feelings of insecurity and a temptation to write "click bait". I think the only really meaningful "metrics" are whether a post generates some useful discussion, someone learns something, or even changes their mind.

Go for the long haul.
Many people start blogs but quickly give up because they don't get much feedback. After about four years I was really wondering whether many people were reading this blog or whether it was having much impact. Then on an international trip, I kept meeting people who read it and thanked me for it. This provided motivation to keep going.

Most readers enjoy a diverse range of subjects.
That is the feedback I received from many readers, as I traverse from the technicalities of constructing diabatic states to mental health to teaching philosophy to ranting about metrics .... Obviously, some posts will be of more interest to some readers than to others. Don't worry about it.

Find ways to stimulate discussion in the comments section
This is probably my only regret. I was too slow to ask readers questions, to engage in discussion with commenters and to allow anonymous comments. On the one hand, I have not attracted as many comments as I would like. I am quite "jealous" of some of the discussions that people like Peter Woit, John Quiggin, and Peter Enns [there is an interesting mix of three people!] can generate. On the other hand, I have been blessed by the absence of trolls or the inane comments or abusive debates that seem so common on many blogs, youtube, and newspaper websites. The only comments I have felt the need to delete are spam advertising. But maybe I am not controversial enough to generate heated debate. One thing I do have to discipline myself is to not "name and shame" scientists and administrators that I think are charlatans. There are also certain topics I just avoid because it tragically seems almost impossible to have a civil online discussion and I am too scared of getting "condemned" for life for exploring some nuanced view that is "offensive", whether to people on the left or on the right.

Keep the software and formatting simple
There are endless possibilities for flashy formats. I am sticking with the most basic format. There are plenty of popular and valuable blogs (e.g. John Quiggin and Peter Woit) that also use rudimentary formats. I suspect wordpress may be better than because it does give more reliable and wider statistics.

Do readers or bloggers have other suggestions for someone about to start out?

Thursday, October 11, 2018

Key ideas in solid state physics

I have had some interesting discussions with an editor at Oxford University Press about the Very Short Introductions series. The upshot is that I have been asked to write a VSI Condensed Matter Physics. I find it amazing and concerning that after 500 titles there wasn't one about CMP. There are excellent ones on Magnetism, Superconductivity, Complexity, and Crystallography.
I am very happy about this and will post more about it later. At first, we discussed a VSI on Solid State Physics. Here is my outline for that.

1. Introduction
    Solid state physics
   - is central to technology (diodes, transistors, LEDs, photovoltaic cells, and computer memories)
   - provides important lessons in scientific model building
   - is one of the largest fields of physics
   - is a rich source of ideas and concepts that have cross-fertilised with other fields of science

2. Solids are quantum matter
Solids are made of atoms (nuclei and electrons).
Electrons are waves. Electrons are fermions. Quantum degeneracy
How is a metal like a white dwarf star?

3. Symmetry matters
Crystal structures. Think in reciprocal space, not in real space.
Why is it possible to determine a crystal structure from x-ray diffraction?
Internal symmetries of electrons: spin, gauge symmetries.

4. Electron waves in a crystal
Bragg scattering. Extended states.
Energy gaps: metals, semiconductors, and insulators
Why is copper a metal while diamond is an insulator?
Why can an electron go through a crystal and pass millions of atoms without being scattered?

5. Multitudes of solid phases
Phase diagrams. Allotropes.
When is graphite less stable than diamond?
Magnetic and superconducting phases
Classifications of phases through "broken symmetry"

6. Emergence
Quasi-particles: electrons and holes, phonons, magnons
How does structure (chemical and crystal) determines electronic and structural properties?
Why does magnesium seem to have positively charged electrical currents?

7. Beyond perfect infinite crystals
a. Impurities, disorder, localisation, glasses: the value of imperfection
b. Flatland. Surfaces and dimensionality

8. Topology matters
Quantum Hall effects, Topological insulators, Quantum magnetism

9. Solid state technology
 Diodes, transistors, LEDs, photovoltaic cells, and computer memories

10. Solid concepts
What have we learned about scientific model building?

This is too much. But what would you add or subtract?

Monday, September 24, 2018

A balanced response to dramatic change

There is no doubt that the world is changing very rapidly. This is true in many spheres: technology, politics, economics, and social. These changes present significant challenges to individuals, families, communities, businesses, institutions, and countries. On this blog there have been many posts and comments about how science and universities are changing.

I think there are three common mistakes in how people respond to these changes.

1. Denial. Claim that the changes are not really that significant (either qualitatively or quantitatively) and we should just keep on operating in the same way. This response will mostly come from those who are not directly affected in the short term.

2. On the other hand, some claim everything has changed and that everything is up for grabs, and they begin to lose sight of basic truths and goals, whether it is human aspirations or the content of physics curricula.

3. Seduction by the "change merchants." These are the opportunists: who want to use the change as a pretext to sell and implement their "solutions" from which they will increase their power, social status, or bank account.

Friday, September 14, 2018

Publishing for Majority World academics

Tomorrow I am giving a talk about academic publishing for a group of faculty and Ph.D students from African universities. The challenges they face are formidable.
Here are my slides.
As always, it is important not to reinvent the wheel.
There are already some excellent resources and organisations. 
A particularly relevant organisation is AuthorAID which is related to inasp, and has an online course starting right now.

Publishing Scientific Papers in the Developing World is a helpful book, stemming from a 2010 conference.
Erik Thulstrup has a nice chapter "How should a Young Researcher Write and Publish a Good Research Paper?"

Wednesday, September 12, 2018

Humility in science

Scientists often like to talk about how much they know and understand. On one level this is fine and appropriate because it is truly amazing how much we do now know and understand about the material world. Yet there are many things we don't really understand, and in some cases it may be argued we may never (at least in our lifetimes) understand certain things.
Furthermore, the preponderance of hype in science today tends to obscure and confuse what we don't understand. Humility can be a good thing for at least two reasons. First, it makes us more open to seeing our mistakes and misunderstandings. Maybe some things we think we do know and understand we may actually be wrong about. Second, in contrast to hype, humility helps us more clearly see and acknowledge the limitations of our current knowledge, so that we can explore ways forward.

Economics is an interesting case. My son, pointed out this quote from Hayek, a Nobel Laureate.
“The curious task of economics is to demonstrate to men how little they really know about what they imagine the can design.”
Friedrich A. Hayek, The Fatal Conceit: The Errors of Socialism

A concrete illustration of this ignorance is illustrating by considering the basic (and very important) question, ``Does government stimulus spending actually produce economic growth?"
Economists cannot agree on the answer. This issue is nicely discussed in a podcast at Econtalk. Jim Manzi ``argues for humility and lowered expectations when it comes to understanding causal effects in social settings related to public policy.''

The physical sciences are blessed with "controlled experiments" and the fact that physical systems seem to be a lot "simpler" than social systems. Nevertheless, that does not justify hype rather than humility.

Monday, September 10, 2018

What can students learn from an Ising model simulation?

Computer simulations can provide significant insight into different physical phenomena. Two decades ago the best one could do in a class or seminar was show screen shots of simulations and try and explain what was going on. Now one can show a simulation live and even vary parameters in real time to provide insight. I have done this quite a bit with Solid State Simulations.

One simulation I like but have never used effectively is that of the Ising model.
See for example, Daniel Schroeder's simulation or James Sethna or Matt Bierbaum.
What does it help me understand?
The main ideas are the concept of symmetry breaking, the correlation length, and the divergence of the correlation length at the critical point.

1. Watching the different configurations changing with time illustrates the notion of an ensemble.
2. At high temperatures one sees the paramagnetic phase where the spins are independent of each other and so there are no domains.
3. As the temperature approaches the critical temperature (T=2.27J) from above the correlation length increases and large fluctuating domains form.
4. Below the critical temperature large domains form and fluctuate less and less as the temperature lowers.
5. The ferromagnetic ground state (blue or yellow, up or down spin) in zero external field depends on the history. This illustrates symmetry breaking

Any other things?

Wednesday, September 5, 2018

Superconductivity in a Hund's metal

The BCS theory of superconductivity is one of the towering intellectual achievements of the twentieth century. There are many ingredients to the theory and many significant results. One key step is to consider an effective interaction that is responsible for the Cooper pairing. A key result is that many properties are universal in that one can rescale temperatures and energies by the energy gap (at zero temperature), Delta(0) or the transition temperature Tc. In the limit of weak-coupling there is a universal ratio
2 Delta(0)/kTc = 3.5
Most elemental superconductors are consistent with this value. Some such as Hg and Pb have larger values, but these can actually be calculated when strong coupling effects are taken into account, via the Eliashberg equations.

Unconventional superconductors (cuprate, organic, heavy fermion, iron based) have resisted a simple unifying theory and universal trends, comparable to the stellar success of BCS theory. For example, the gap/Tc ratio is all over the place. However, there has been some progress for the iron-based superconductors. Recent ARPES results (summarised in the figure at the bottom below) have shown a universal ratio, of about 7.2 for a wide range of materials.

A fascinating feature of these iron-based materials is the nature of the metallic state that undergoes the superconducting instability. I have written several blog posts about the Hund's metal. One important feature is that there is relatively low coherence temperature below which a Fermi liquid metal forms, and there is a correspondingly low energy scale Omega0 associated with spin fluctuations, which become very slow. This arises from the rich Kondo physics associated with the multi-orbital character of the system. Furthermore, the spin fluctuation spectrum has a power law dependence above Omega0.

The above ideas come together in an interesting preprint
On the Superconductivity of Hund's Metals 
Tsung-Han Lee, Andrey Chubukov, Hu Miao, Gabriel Kotliar

They consider a single band superconductor described by the strong-coupling Eliashberg equations where the frequency dependence of the (effective) electron-electron attraction is given by
where the exponent gamma is treated as a variable. The Eliashberg equations are solved (for a single band) and give the following relationship between the gap ratio and the exponent gamma.
The value of gamma=1.2 is that associated with the relevant Kondo problem above the coherence temperature. The gap ratio corresponds to the black dashed line in the graph below.

One thing should be stressed here is that one is observing a transition from an incoherent metal into a superconductor, unlike in the BCS situation where the transition is from a coherent Fermi liquid.
I thank Alejandro Mezio for bringing the paper to my attention.

Monday, September 3, 2018

Absurd to the n'th degree, not chemical cricket

It is easy to take for granted many scientific ideas and results that seem commonplace and reasonable to us today. However, when some ideas were first proposed or discoveries made they were greeted with scepticism, and even ridicule.

In 1913 the Braggs determined the crystal structure of sodium chloride. They were awarded the Nobel Prize in Physics in 1915. However, as late as 1927, the following letter appeared in Nature.

[Double click if you want to read a larger version].

I recently became aware of this in Crystallography: A Very Short Introduction by A.M. Glazer.

Thursday, August 30, 2018

The mental health crisis among university students is going to get worse

For the past few months I have been travelling in North America and the UK, for a mixture of work and holiday. In a range of professional and social settings I have had conversations with different people associated with universities: faculty, students, parents, and NGOs. It is amazing (and disturbing) how many times one subject keeps coming come up: student mental health problems. It was never me who brought up the subject and I don't think any of the people who did bring it up knew that I am interested in the issue, partly because of my own struggles. Two important questions people have asked are:

Has the incidence of student mental health problems increased or is it just that reporting of problems has increased?

Is the situation likely to improve in the near future?

Unfortunately, I think the problems have substantially increased and that they unlikely to decrease in the near future. I hope I am wrong. But, I think that there are a multitude of inter-related social, economic, and political changes that form a toxic cocktail for students.

To illustrate the extent of the problem and some of the compounding issues it is worth reading these two articles, both of which almost have a (tragic) surreal feel.

Why are suburban super-students burning out in college? These Main Line therapists say anxiety is high – and all around us
Philadelphia Inquirer

Feeling Suicidal, Students Turned to Their College. They Were Told to Go Home
New York Times
[Comments are worth reading too]

What are the origins of the crisis?
I think it may be a combination of the factors below. In isolation I doubt one or two of them would create such a large problem, but when you put many together, life starts to get very difficult. To what extent you think some of them is a problem may also depend on what you believe is "normal" and "healthy". The factors are listed in random order. Some are inter-related.

A winner takes-all society.
Everyone wants to be a winner and a celebrity. But most people are not. At the crass level, this cultural shift is reflected in TV shows involving singing or cooking competitions. It is also reflected in increasing economic inequality,  where the wealth of the upper class (the one per cent) is increasing dramatically and the lower middle class is ballooning, including graduates with massive debts from student loans. The pressure to succeed is immense and the despair of "failure" is greater.

Social media.
Students are comparing themselves to their "friends" and struggling to project a perfect and successful life. Interpersonal conflict is escalated because social media is a flawed medium for civil and meaningful communication. Rather that talking to other students before or after class students are staring at their phones.

Frustration from or fear of unfulfilled expectations.
University marketing departments portray life on campus as a collection of beautiful young people sitting around on lawns on bright sunny days having meaningful conversations before they graduate to high-paying and fulfilling jobs. A student at an over-crowded state university soon discovers they are sitting in a lecture hall with hundreds of students and no one seems to care whether they are there or not. Although they were told their degree would be a launching pad for a "career", many discover it is actually hard to get any sort of job, let alone something related to their major. No wonder they are depressed!

Excessive screen time.
It is bad for your brain and addictive. You get overstimulated. For some there is addictive content such as on-line games and pornography. It cuts into time for personal relationships.

Breakdown of family life.
Parents are increasingly absent, whether literally, emotionally, or practically, while children are growing up. This decreases students sense of identity, stability, ability to navigate life, including form meaningful relationships, and resolve conflict.

Alcohol and drug abuse.
This may actually be decreasing. However, it is still rampant, and compounds all of the other problems. Furthermore, mental health problems and substance abuse become intertwined.

Sexual harassment and assault.
Reporting has certainly increased. Again, the prevalence of this problem compounds all of the issues above.

What do you think? Have the problems increased? If so, what are the causes?

Wednesday, August 22, 2018

Basic introductions to Condensed Matter Physics

Suppose a motivated and intelligent high school student or first year undergraduate comes to you and says, ``Condensed matter physics sounds really cool! What should I read or look at to learn more about it?"

Obviously, suggesting the student look at classic graduate texts such as Ashcroft and Mermin or Chaikin and Lubensky is not helpful. They need something that will inspire them to want to learn more as well as introduce them to some of the basic ideas and topics.

I would suggest the following.

David Pines, Unit 8 in Physics for the 21st Century, an on-line course
Emergent Behavior in Quantum Matter

Robert Laughlin, A Different Universe: Reinventing Physics from the Bottom Down

Stephen Blundell, Superconductivity: A Very Short Introduction

Rodney Cotterell, The Material World

But when then have read some of these it would be nice if the student could look at something more technical. To second year undergrads I give a series of lectures on Thermodynamics and Condensed Matter Physics. They don't need to know any quantum or stat. mech., just some thermo, and they can still get some of the flavour, excitement, and scope of the subject. But, I don't know a book that lays this material out clearly and simply. I draw on Schroeder, Thermal Physics, but it has no discussion of superfluids, order parameters, or symmetry breaking.

What do you think are good resources?

I thank Alex Agedah for asking this question.

Update. Here are some slides for a talk that Danielle McDermott gave on the subject. It lists many useful resources. (She mentions it in a comment below).

Sunday, August 19, 2018

Big changes in universities?

I was recently asked to give a talk to an NGO about how universities are changing.
There is no doubt that there are rapid changes, many for the worse, happening. For me the biggest change has been the rising influence of neoliberalism (free market ideology) in the values, goals, and decision making within universities. But that is another story...
In the past few weeks some relevant articles "came across my desk" [through my web browser...].

I would be particularly interested to hear readers comments on the first one.
My wife sent me this New York Times piece to read and I really despaired
The iGen Shift: Colleges Are Changing to Reach the Next Generation 
The newest students are transforming the way schools serve and educate them, including sending presidents and deans to Instagram and Twitter.

Why do I despair?
I believe a university education should largely be about two things. The first goal is explicit and the second is implicit.

The first and primary goal of university education is to help students to learn to think: to think about specific disciplines, and to think about anything. Deep and valuable thinking does not come easily. It takes time, concentration, perseverance, and freedom from distractions. It a student is constantly checking their phone or just skimming the first material that comes up on a Google search or in the Twitter (for twits!) feed for their course, it is highly unlikely they are going to do much deep thinking.

Second, a university education is about helping students "grow up":  to move towards adulthood, to learn to be responsible and independent, to create an identity that is more independent of their parents and their peers, to have a sense of direction and purpose, and a desire to be good citizens.
Unfortunately, too many students think "growing up" means getting really drunk and throwing up...
However, too many of the initiatives described in the article seem to be pandering to students (customers) and "hand holding" them through their university experience. For example, at some point in life students are going to have to learn to seek and find relevant information, regardless of whether it is nicely packaged in some cool app with great graphics and lots of "likes".

Oh, the Humanities! 
New data on college majors confirms an old trend. Technocracy is crushing the life out of humanism.
Ross Douhat (NYT op-ed columnist)

The third article is more controversial and political, and raises questions about whether one purported change is as big or significant as often claimed (particularly in the right-wing press)
The free speech panic: how the right concocted a crisis
Snowflake students have become the target of a new rightwing crusade. But exaggerated claims of censorship reveal a deeper anxiety at the core of modern conservatism.
William Davies (A Long Read in The Guardian)
For balance here is a counter-view that there is a problem
The Problem of Hyper-liberalism
John Gray (Times Literary Supplement)

Comments welcome.

Wednesday, August 15, 2018

Solid State or Condensed Matter Physics?

The two terms are often used interchangeably, but that is not appropriate. Condensed matter physics does not just involve solids but also phenomena in liquids, liquid crystals, superfluids, and polymer melts.  Solid state physics is a subset of condensed matter physics. The latter term was arguably coined by Phil Anderson, when he and Mott renamed their research group at Cambridge in the 1970s. One can view research fields or course titles as a list of topics or as a way of thinking about certain parts of reality. Solids exhibit rich phenomena including magnetism and superconductivity. However, it is best to actually view the solids as (an almost irrelevant) substrate for the phenomena.

Like many things, this perspective arguably started with Landau. His theory of phase transitions in the 1930s did not consider atomic structure or chemical composition. Even structural phase transitions were viewed in terms of symmetry change, not in terms of explicit microscopic details. In 1950 this led to the Ginzburg-Landau theory of superconductivity. This all suggested a unified approach to phase transitions.
Furthermore, Landau's Fermi liquid theory papers were originally concerned with understanding liquid 3He, not electrons in metallic crystals.

This idea was further highlighted in the 1970s with the study of critical phenomena and the associated idea of universality. Specifically, the critical behaviour of an XY magnet, a superconductor, and a superfluid, are the same (i.e. they have the same critical exponents). The critical behaviour of the liquid-gas transition, an Ising magnet, and the order-disorder transition in a binary alloy are the same. The view that the solid state might actually not be the key feature for understanding and describing superconductivity was highlighted in the 1950s by Fritz London in his two-volume book, Superfluids, which suggested the two phenomena were intimately connected. Beginning in 1968, De Gennes took a condensed matter perspective in applying order parameters and scaling ideas to “soft matter”: liquid crystals, polymers, wetting, …

The important element to this conceptual view of condensed matter is that it provides a unifying perspective on phenomena in a diverse range of materials. It also brings to the fore how a wide suite of powerful theoretical and experimental tools (esp. neutron and x-ray scattering) can be used to study diverse materials. One of the key theoretical strategies is that of effective Hamiltonians, which is not unique to condensed matter, because it just reflects the hierarchy of energy, length, and times scales that result from emergence. This then leads to an intellectually rich interchange of ideas and techniques from other fields of physics, particularly quantum field theory.

More recently, this unity is illustrated by ultracold atomic gases which can be used to study some phenomena that had previously only been studied in solids.

Saturday, August 11, 2018

Hype, DNA, drugs, and emergence

Unfortunately, hype in science reflects hype in broader society, including in business. The complete DNA sequencing of the human genome was an amazing scientific achievement. Unfortunately, it was also associated with a lot of hype about what this would mean for medicine and for the pharmaceutical industry. This issue is made painfully and succinctly in a recent column in the business section of  The Guardian by Nils Pratley.
It has been almost two decades since the first bosses of the newly merged GlaxoSmithKline talked up the medical wonders that would flow from the unravelling of the human genome. GSK would become the “Microsoft of the pharmaceutical industry”, they said.  
To put it mildly, the corporate vision hasn’t been realised. GSK’s share price stood at £20 at the time of the turn-of-the-century merger and is £15.42 today. Lack of productivity in the labs has been a constant complaint. The genetics revolution is happening, but not at the pace originally promised, at least not at GSK.
These challenges could have been forseen by filtering the hype through a emergentist perspective, such as that presented beautifully by Denis Noble in a 2006 book, The Music of Life: Biology beyond the Genome.  Knowing a DNA sequence is about as useful, for better or worse, as knowing the many-body Schrodinger equation for a plutonium crystal. A great place to start, but ....

Thursday, August 9, 2018

Emergent temperature scales and spin-orbital separation in the Hund's metal

An important and fascinating issue in many-body physics is the emergence of new energy scales, particularly scales that are orders of magnitude smaller than the energy scales in the underlying Hamiltonian. One example is the coherence temperature associated with the crossover from a Fermi liquid (with coherent quasi-particles) to a bad metal.

Recently, I posted about the crossover from a Hund's metal to a bad metal, seen in the collapse of the Drude peak in the optical conductivity, and the issue of capturing this slave-particle theories. One commenter mentioned the relevance of the paper below and another asked about the claim that the Kondo effect is associated with the collapse.

I agree that Kondo physics is associated with the crossover. Although, far from obvious this is also the case in the single-band Hubbard model. The Kondo effect was first studied with isolated magnetic impurities in metals and can be described by a single-impurity Anderson model (SIAM). Although there are no magnetic impurities in the Hubbard model, it turns out that when studied at the level of Dynamical-Mean-Field Theory (DMFT), the model is described by a self-consistent SIAM and close to the Mott metal-insulator transition Kondo physics does emerge. Specifically, the Kondo temperature for the self-consistent SIAM corresponds to the temperature at which there is a crossover from local unscreened local magnetic moments (associated with the almost-localised electrons near the Mott phase; the bad metal) to a Fermi liquid where the "magnetic moments" are screened.

What happens in a two-band Hubbard-Kanamori model with Hund's rule coupling?
The physics is richer because there is now the possibility screening of spin and/or orbital degrees of freedom, and of a orbital-selective Mott phase (or bad metal). 
This is nicely investigated in the following paper.

Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal
K. M. Stadler, Z. P. Yin, J. von Delft, G. Kotliar, and A. Weichselbaum

For me, the figure below is the most interesting and illuminating. It shows how due to the Hund's rule coupling, two distinct energy scales (differing by about two orders of magnitude) emerge and associated with screening the spin and orbital degrees of freedom, respectively.

This is Kondo physics, but there are no magnetic impurties.

Tuesday, August 7, 2018

Philosophy and emergence in condensed matter

Condensed matter physics is a source of a multitude of beautiful examples of emergence.  On the other hand, for more than a century philosophers have thought seriously about emergence, partly motivated by profound and difficult questions concerning human consciousness and free will.
Prior to the past decade, there appear to have been no substantial interactions between physicists and philosophers about the subject. A few years ago I posted about some recent work by philosophers of science on quasi-particles.

One of the big issues that philosophers wrestle with is the relative merits of weak emergence and strong emergence, which are sometimes distinguished as epistemological and ontological emergence.

I am very happy that in the past year or so that philosophy journals have published more than half a dozen papers about emergence in condensed matter. One of the papers, by Stephen Blundell, I blogged about earlier. Here I will mention two others and discuss one. All the papers are a result of the Durham Emergence Project.

Strong emergence and downward causation in biological physics
Tom C. B. McLeish

Reduction and emergence in the fractional quantum Hall state 
Tom Lancaster and Mark Pexton

McLeish begins with a helpful and succinct summary of the argument by Jaegwon Kim about "the causal completeness of the physical" [or the argument against non-reductive physicalism] that leads to the conclusion that mental events cannot have physical consequences. This argument has attracted significant attention from philosophers and has been used against strong emergence, and particularly to argue that consciousness is reducible.

McLeish rightly points out that the problem of consciousness is a "can of worms" [my phrase] and instead it might be valuable to consider the issue of "downward causation" by considering three important examples in biological physics.

"Downward causation" means "there are high-level entities, carrying unique information about the system essential for its future evolution, and whose form and evolution are not determined entirely by the low level entities."
He gives a nice introduction to soft matter physics and its applications to biological systems, considering the following examples.
  • Membrane and intra-membrane self-assembly
  • Allosteric Signalling in Gene Expression
  • Entangled DNA and Topoisomerases  
He points out how in these systems there is "top down causation" and that the emergent entities such as protein elasticity are not just a result of "coarse graining" but new "long-range physics" that arises from many microscopic realisations.

McLeish considers these examples reflect what Bishop and Silberstein (2016) defines as ``‘epistemological contextual emergence’ (ECE) as applying to systems whose ...description at a particular descriptive level (including its laws) offers some necessary but no sufficient conditions to derive the description of properties at a higher level.''

I thank Stephen Blundell and Tom McLeish for helpful discussions about their papers.

Thursday, August 2, 2018

Phase diagram of snowflakes

I like "collecting" interesting phase diagrams, partly because they are fun to show students when teaching introductory thermodynamics. I recently discovered the one below that I feel I really should have known about. It shows the morphology of different snow crystals as a function of temperature and water supersaturation (relative to ice).
It should be pointed out that this is a non-equilibrium phase diagram as it involves supercooled liquid water.

The figure below is taken from the beautiful review
The physics of snow crystals 
Kenneth G Libbrecht

This diagram was originally constructed by Ukichiro Nakaya in the 1930's. The physics behind it is still poorly understood.

I came across the diagram while browsing through the Forces of Nature book by Brian Cox and Andrew Cohen.

While on the subject here is a nice video.

Monday, July 30, 2018

Experimental observation of the Hund's metal to bad metal crossover

A definitive experimental signature of the crossover from a Fermi liquid metal to a bad metal is the disappearance of a Drude peak in the optical conductivity. In single band systems this occurs in proximity to a Mott insulator and is particularly clearly seen in organic charge transfer salts and is nicely captured by Dynamical Mean-Field Theory (DMFT).

An important question concerning multi-band systems with Hund's rule coupling, such as iron-based superconductors, is whether there is a similar collapse of the Drude peak. This is clearly seen in one material in a recent paper

Observation of an emergent coherent state in the iron-based superconductor KFe2As2 
Run Yang, Zhiping Yin, Yilin Wang, Yaomin Dai, Hu Miao, Bing Xu, Xianggang Qiu, and Christopher C. Homes

Note how as the temperature increases from 15 K to 200 K that the Drude peak collapses. 
The authors give a detailed analysis of the shifts in spectral weight with varying temperature by fitting the optical conductivity (and reflectivity from which it is derived) at each temperature to a model consisting of three Drude peaks and two Lorentzian peaks. Note this involves twelve parameters and so one should always worry about the elephants trunk wiggling.
On the other hand, they do the fit without the third peak, which is of the greatest interest as it is the sharpest and most temperature dependent, and claim it cannot describe the data.

The authors also perform DFT+DMFT calculations of the one-electron spectral function (but not the optical conductivity) and find it does give a coherent-incoherent crossover consistent with the experiment. However, the variation in quasi-particle weight with temperature is relatively small.

Tuesday, July 24, 2018

Maximise your comparative advantage

A snarky mathematician [Stanislaw Ulam] once challenged the great Paul Samuelson to name an economic proposition that is true but not obvious. Samuelson’s choice was comparative advantage, which shows, among other things, that there are mutual gains from trade even if one nation is better than another at producing everything.  
 Here’s a homespun illustration. Suppose a surgeon is also a whiz at house painting—better than most professional painters. Should she therefore take time off from her medical practice to paint her own house? Certainly not. For while she may have a slight edge over most painters when it comes to painting walls, she has an enormous edge when it comes to performing surgery. Surgery is her comparative advantage, so she should specialize in it and let some others, who don’t know their way around an operating room, specialize in painting—their comparative advantage. That way, the whole economy becomes more efficient.  
 The same principle applies to nations. Even if China could manufacture everything more efficiently than the U.S. can (which it can’t), it would still make sense for the U.S. to specialize in the goods in which it has comparative advantages, and then trade with China for the things it wants but doesn’t produce. Both countries wind up getting more for less.
Alan Blinder
A Brief Introduction to Trade Economics 
Why deficits are normal, especially for a country like the U.S., and what is comparative advantage.

It is worth considering the relevance of the concept of comparative advantage to doing science and its administration.

Individual scientists, should identify their comparative advantage [e.g. a particular technique, a sub-field, approach, instrument, ...] and maximise it. Furthermore, they may be better than their grad students at doing certain things, but that does not mean they should do those things.
Some exceptional scientists may be good at public outreach and chairing committees but they need to be careful such things don't stop them from doing the science for which they have a clear comparative advantage.

Collaborations should also make sure individuals maximise their comparative advantage. A collaboration may also have a particular comparative collective advantage [e.g. combined theory and experiment, chemists and physicists, ...].

Yet, there is significant sociological pressure against maximising comparative advantage for the good of science as a whole. For example, the pressure to publish more papers may lead to a gifted individual focusing on low-lying fruit and publons, rather than maximising their competitive advantage to tackle and solve difficult problems with patience and creativity.
The pressure to work on fashionable topics (e.g. to boost citation indices or get funding) may pressure scientists to leave fields in which they have comparative advantage.

Administrators should think twice before increasing the pressure on scientists to do more of their own administration, lab maintenance, public outreach, IT support, secretarial work, ...
These are not things in which they have a comparative advantage.

Saturday, July 21, 2018

Questions about slave-particle mean-field theories of Hund's metals

One of most interesting new ideas about quantum matter from the last decade is that of a Hund's metal. This is a strongly correlated metal that can occurs in a multi-orbital material (model) as a result of the Hund's rule (exchange interaction) J that favours parallel spins in different orbitals.
Above some relatively low temperature (i.e. compared to the bare energy scales such as non-interacting band-widths, J, and Hubbard U) the metal becomes a bad metal, associated with incoherent excitations.
An important question concerns the extent to which slave mean-field theories can capture the stability of the Hund's metal, and its properties including the emergence of a bad metal above some coherence temperature, T*.

In a single-band Hubbard model, the strongly correlated metallic phase that occurs in proximity to a Mott insulator is associated with a small quasi-particle weight and suppression of double occupancy, reflecting suppressed charge fluctuations. This is captured by slave-boson mean-field theory, including the small coherence temperature.

In contrast, to a "Mott metal", a Hund's metal is associated with suppression of singlet spin fluctuations on different orbitals, without suppression of charge fluctuations and is seen in a Z_2 slave-spin mean-field theory at zero temperature.

Specific questions are whether slave mean-field theories at finite temperature can capture the following?
  • The coherence temperature, T*.
  • A suppression of spin singlet fluctuations at T increases towards T*.
  • An orbital-selective bad metal may occur in proximity to an orbital selective Mott transition. This is where at least one band (orbital) is a Fermi liquid and another is a bad metal. This would mean that there are two different coherence temperatures. 
  • The emergence of a single low-energy scale, common in both bands, as is seen in DMFT.
  • The spin-freezing temperature.
Finally, how does the stability of the Hund's metal change with the number of orbitals?
Figures in this post suggest that the Hund's physics is more pronounced with increasing the number of orbitals. However, that may be because the critical U (and thus proximity to the Mott insulator) changes with the number of orbitals and all the curves are for the same U.

Thursday, July 19, 2018

It's not complicated. It's Complex!

When is a system "complex"?
Even though we have intuition (e.g. complexity is associated with many interacting degrees of freedom) coming up with definitive criteria for complexity is not easy.

I just finished reading, Complexity: A Very Short Introduction, by John Holland.
His perspective is that a system is "complicated" if it has many interacting degrees of freedom, but is "complex" if in addition it exhibits emergent properties.
The criteria for emergence is the existence of new hierarchies, containing new entities or agents (defined by the formation of boundaries) that are coupled by new interactions, and described by new "laws".

Holland distinguishes complex physical systems (CPS) from complex adaptive systems (CAS).
The latter involve elements (agents) that can change (learn or adapt) in response to interactions with other agents.
Cellular automata and pattern formation in biology are CPS, whereas genetic algorithms, economics, and sociology are examples of CAS.

The book gives a rather dense (but worthwhile) introduction to key concepts in complexity theory including the emergence of specialists (e.g., division of labor, according to Adam Smith in economics), the role of diversity, co-evolution (e.g. Darwin's orchid and moth), and evolutionary niches (fixed points of Markov matrices!).

Holland smoothly flits backwards and forwards between examples in biology, economics, linguistics, and computer science.

Holland's definition of emergence is consistent with how I think in condensed matter. For example, the formation of weakly interacting quasi-particles in a Fermi liquid. The emergent "boundaries" define the spatial size of the quasi-particle.
What struck me is that the interactions should be viewed as emergent, just as much as the quasi-particles.
For example, if we start with quarks and QCD (quantum chromodynamics), then at "low" temperatures and densities, nucleons form and the nuclear force emerges.

Tuesday, July 17, 2018

How do you get in a productive zone?

We all want to increase our productivity. But too often we are distracted, procrastinate, stressed, or waste time going down dead ends.
I think there are two distinct kinds of productivity.
The first is creative, where we can clearly conceive a project, solve a problem, or draft a useful outline.
The second is the actual completion of a task, whether writing a paper or report, or making corrections, ... This is less creative and more mundane, but can consume large amounts of time, particularly if one stops and starts on the task many times.

How might you increase your productivity?
I think this is quite personal and maybe even somewhat random.
It might be very different for different people. It can be different at different times.
Factors to consider include the following.

Physical space and environment. 
Some people need a regular quiet work space that is free from distractions. Others will function well in a noisy cafe or an open plan office, maybe with headphones with loud music!

Some people function well with deadlines. Others crumble under the pressure. Some work well with short bursts during the day. Others need to block out a day or even a week to focus on something.

Involvement of others.
Some people will work best alone on a task, with minimal interactions with others. Others will barely function without input and feedback from others at many points in the process.

Good managers are sensitive to this diversity of needs and will aim to provide the appropriate environment for different individuals.

This post was stimulated by a recent experience how something came together and I was able to get a lot of work done on a specific task during a couple of plane flights. This seemed a bit random because these days I rarely work on flights because it is really non-productive.

What do you think?
What helps you get in the right "zone"?

Sunday, July 8, 2018

Square ice on graphene?

As I have written many times before, water is fascinating, a rich source of diverse and unusual phenomena, and an unfortunate source of spurious research reports.
Polywater is the classic example of the latter.
I find the physics particularly interesting because of the interplay of hydrogen bonding and quantum nuclear effects such as zero-point motion and tunneling.

There is a fascinating paper
Polymorphism of Water in Two Dimensions
Tanglaw Roman and Axel GroƟ

The paper was stimulated by a Nature paper that claimed to experimentally observe square ice inside graphene nanocapillaries. Such a square structure is in contrast to the hexagonal structure found in regular three-dimensional ice.
Subsequent, theoretical calculations claimed to support this observation of square ice.
Here the authors use DFT-based methods to calculate the relative energies of a range of two-dimensional structures for free-standing sheets of water (both single layer and bilayers) and for sheets bounded by two layers of graphene.

The figure below summarises the authors results for free-standing layers showing how the relative stability of the different water structures depends on the area density of water molecules [which varies the length and strength of the hydrogen bonds].

On the science side, there are several interesting questions arise.
How much do the results depend on the choice of DFT functional used [RPBE with dispersion corrections]?
Would inclusion of the nuclear zero-point energy modify the relative stability of some of the structures, as it does for the water hexamer?
Quantum nuclear effects are particularly important when the hydrogen bond length [distance between oxygen atoms] is about 2.4 Angstroms. [I am not quite sure what area density this corresponds to for the different structures].

On the sociology side, this paper is another example of a distressingly common progression:
1. A paper in a luxury journal reports an exotic and exciting new result.
2. More papers appear, some supporting and some raising questions about the result.
3. A very careful analysis reported in a solid professional journal shows the original claim was largely wrong. This paper attracts few citations because the community has moved on to the latest exciting new "discovery" reported in a luxury journal.

I thank Tanglaw Roman for helpful discussions about his paper.