Wednesday, May 30, 2018

Broken symmetry, order, and entropy

One of the greatest joys of teaching is having students ask questions that you do not know the answer to. In the last week of the course PHYS2020 Thermodynamics and Condensed Matter Physics for second year undergrads at UQ, I give two lectures about critical points, universality, critical exponents, broken symmetry, order parameters, and Landau theory.

Many students find this quite challenging. However, I think it is important that students be exposed to two of the most important ideas of theoretical physics from the twentieth century: broken symmetry and universality. Furthermore, there is no technical reason why second year undergrads cannot learn this material. Since the text, Thermal Physics by Schroeder, does not cover this material we have finally settled on a chapter from a book by Hoch.

After my last lecture, a student asked an excellent question along the lines of
"Why is it that broken symmetry occurs at lower temperatures?
How is this related to entropy and order?"

This led me to wondering whether there were any rigorous results that answer the question. I could not find anything in a quick search.
Do you know of anything?

I was wondering whether something like the following conjecture was true:
Conjecture. Consider a physically reasonable Hamiltonian H for an infinite system. Suppose H is invariant under some symmetry group G. Let rho(T) be the equilibrium density matrix at temperature T. Then for sufficiently large T, rho(T) is also invariant under G.
Maybe this is equivalent to
Lemma. At sufficiently high temperatures, the von Neumann entropy S (rho) = - Tr( rho ln (rho)) is maximal if rho is invariant under G. 
This looks to me like the kind of thing that people like Elliot Lieb, David Ruelle, Y. Sinai, ... might have tackled at some point.

I welcome ideas and suggestions.

Monday, May 28, 2018

Pushing back against the multi-versity

One of the many concerns I have about universities, particularly in Australia, is the trend to compartmentalisation, factionalisation, fragmentation, obscure over-specialisation, ...
Long ago visions of the UNIversity included unity of knowledge, collegiality, and combining breadth and depth, ...
This trend to the multi-versity manifests itself in diverse ways:
- the lack of appreciation for the value of a liberal arts education
- students who are reluctant to see the relevance of previous subjects and course they have studied to the one they are studying right now, and more broadly the value of other majors (e.g. maths to physics, physics to chemistry, chemistry to biochemistry, history to sociology, philosophy to everything, ....)
- departments that ruthlessly compete with one another for student enrolments
- a ridiculous diversity of undergraduate majors, minors, and degrees
- claims that all points of view are equally valid and should not be critiqued
- a lack of interest in big ideas, big questions, and big issues

In light of this I was fascinated to read about an initiative of the current President of Princeton, Christopher Eisgruber. The Pre-Read has now been running for six years. Before they arrive on campus all Freshman are sent a copy of the same academic book to read and discuss.
In a recent short article, Eisberger discusses the criteria he uses for selecting the book each year.
 The Pre-read’s author speaks to the incoming class at the Freshman Assembly during Orientation week. The book also forms the basis of my Opening Exercises remarks, and I lead Pre-read seminars in the residential colleges during the fall semester.
His two primary goals are to "introduce students to Princeton's vibrant intellectual culture" and "to encourage students to reflect on the values that should guide their Princeton educations and their lives after graduation''.

There are many things I like about the initiative. One is that it helps encourage civil, robust, and intellectually rigorous debate among the students.
Another positive is that the university president himself interacts with the undergrads about the book. This not only has benefits for the students but also for the President himself (and consequently the whole university) because he is exposed first hand to "coal face". I emphasised this point earlier in a post All University Managers should have to teach.
[Aside. I am very happy that the UQ Provost is currently helping teach an undergrad physics class.].

There is many things that Princeton does that other universities cannot do due to lack of resources. However, this is actually an initiative that almost any university could do.

Do you know of other similar initiatives?

Wednesday, May 23, 2018

Metrics and mental health

I never thought I would write a post linking the two issues in the title.

I have been working on my talk on mental health for the School of Maths and Physics colloquium on friday. Here is the current version of my slides. I welcome any comments.

In my preparation I have become aware of a few more resources. A recent issue of Nature includes several articles, including:

An Editorial, What to do to improve postgraduate mental health.
Four researchers write from their own experience, How to handle the dark days of depression.
There is also A collection of resources.

On the one hand, it is wonderful that Nature is highlighting the issue. On the other hand, it would be nice if they reflected how Nature Publishing Group might actually be part of the problem, as they mindlessly promote metrics and their journals. It is a case of corporate "well-washing."

The link between metrics and mental health is brought out in a report to the Higher Education Funding Council for England: The Metric Tide, Report of the Independent Review of the Role of Metrics in Research Assessment and Management, July 2015. The preface states:
Too often, poorly designed evaluation criteria are dominating minds, distorting behaviour and determining careers. At their worst, metrics can contribute to what Rowan Williams, the former Archbishop of Canterbury, calls a “new barbarity” in our universities. 
The tragic case of Stefan Grimm, whose suicide in September 2014 led Imperial College to launch a review of its use of performance metrics, is a jolting reminder that what’s at stake in these debates is more than just the design of effective management systems. 
Metrics hold real power: they are constitutive of values, identities and livelihoods. 

Monday, May 14, 2018

Conducting metallic-organic frameworks

Thanks to the ingenuity of synthetic chemists metallic-organic frameworks (MOFs) represent a fascinating class of materials with many potential technological applications.
Previously, I have posted about spin-crossover, self-diffusion of small hydrocarbons, and the lack of reproducibility of CO2 absorption measurements in these materials.

At the last condensed matter theory group meeting we had an open discussion about this JACS paper.
Metallic Conductivity in a Two-Dimensional Cobalt Dithiolene Metal−Organic Framework 
Andrew J. Clough, Jonathan M. Skelton, Courtney A. Downes, Ashley A. de la Rosa, Joseph W. Yoo, Aron Walsh, Brent C. Melot, and Smaranda C. Marinescu

The basic molecular unit is shown below. These molecules stack on top of one another, producing a layered crystal structure. DFT calculations suggest that the largest molecular overlap (and conductivity) is in the stacking direction.
Within the layers the MOF has the structure of a honeycomb lattice.

The authors measured the resistivity of several different samples as a function of temperature. The results are shown below. The distances correspond to the size of the compressed powder pellets.

Based on the observation that the resistivity is a non-monotonic function of temperature they suggest that as the temperature decreases there is a transition from an insulator to a metal. Since there is no hysteresis they rule out a first-order phase transition, as is observed in vanadium oxide, VO2.
They claim that the material is an insulator about about 150 K, based on fitting the resistivity versus temperature to an activated form, deducing an energy gap of about 100 meV. However, one should note the following.

1. It is very difficult to accurately measure the resistivity of materials, particularly anisotropic ones. Some people spend their whole career focussing on doing this well.

2. Measurements on powder pellets will contain a mixture of the effects of the crystal anisotropy, random grain directions, intergrain conductivity, and contact resistances. This is reflected in how sample dependent the results are above.

3. The measured resistivity is orders of magnitude larger than the Mott-Ioffe-Regel limit. suggesting the samples are very "dirty" or one is not measuring the intrinsic conductivity or this is a very bad metal due to electron correlations.

4. It is debatable whether one can deduce activated behaviour from only an order of magnitude variation in resistance, due to the narrow temperature range considered.

The temperature dependence of the magnetic susceptibility is shown below, and taken from the Supplementary material.

The authors fit this to a sum of several terms, including a constant term and a Curie-Weiss term. The latter gives a magnetic moment associated with S=1/2, as expected for the cobalt ions, and an antiferromagnetic exchange interaction J ~ 100 K. This is what you expect if the system is a Mott insulator or a very bad metal, close to a Mott transition.

Again, there a few questions one should be concerned about.

1. How does this relate to the claim of a metal at low temperatures?

2. The problem of curve fitting. Can one really separate out the different contributions?

3. Are the low moments due to magnetic impurities?

The published DFT-based calculations suggest the material should be a metal because the bands are partially full. Electron correlations could change that. The band structure is quasi-one-dimensional with the most conducting direction perpendicular to the plane of the molecules.

All these questions highlight to me the problem of multi-disciplinary papers. Should you believe physical measurements published by chemists? Should you believe chemical compositions claimed by physicists? Should you believe theoretical calculations performed by experimentalists? We need each other and due diligence, caution, and cross-checking.

Having these discussions in group meetings is important, particularly for students to see they should not automatically believe what they read in "high impact" journals?

An important next step is to come up with a well-justified effective lattice Hamiltonian.

Thursday, May 10, 2018

David Pines (1924-2018): quantum-many body theorist

I learnt today that David Pines died last week. He was a pioneer in quantum many-body theory, applying it not just to solid state physics but also to nuclear physics and astrophysics (neutron stars).  Furthermore, he was a great advocate of the importance of emergence in science, writing a classic paper, "The Theory of Everything," together with Bob Laughlin.

David also left a legacy of creative new institutions, being a co-founder of the Sante Fe Institute and the International Institute for Complex Adaptive Matter (I2CAM). Indeed, starting this blog was stimulated by David Pines and I2CAM. In January 2009, I attended the annual meeting of I2CAM in Cambridge and David organised a session on public outreach, including a presentation on blogging.

Piers Coleman, a current co-Director of I2CAM, has written a nice obituary which gives more details about David's contributions, both scientific and institutional.

Friday, May 4, 2018

Metric madness outside the university

Universities are going off the rails because of the blind use of metrics. Unfortunately, this reflects what is also happening in wider society, due to the rise of neoliberalism.
Australia has recently been rocked by scandals involving large banks, leading to the resignation of CEO's, Board chairs, lawyers, ...

This stimulated the following column, by Ross Gittins, the Economics Editor of the Sydney Morning Herald. It is worth reading in full, but I reproduce a few choice extracts.
Banks' misbehaviour shows power of KPIs
... though the financial services industry must surely be the most egregious instance of the misuse of performance indicators and performance pay, let’s not forget “metrics” is one of the great curses of modern times.
It’s about computers, of course. They’ve made it much easier and cheaper to measure, record and look up the various dimensions of a big organisation’s performance, as well as generating far more measurable data about many dimensions of that performance.
Which gave someone the bright idea that all this measurement could be used as an easy and simple way to manage big organisations and motivate people to improve their performance. Setting people targets for particular aspects of their performance does that. And attaching the achievement of those targets to monetary rewards hyper-charges them. Hence all the slogans about “what gets measured gets done” and “anything that can be measured can be improved”. 
Thus have metrics been used to attempt to improve the performance of almost all the major institutions in our lives: not just big businesses, but primary, secondary and higher education, medicine and hospitals, policing, the public service – the Tax Office and Centrelink, for instance. Trouble is, whenever we discover new and exciting ways of minimising mental effort, we run a great risk that, while we’re giving our brains a breather, the show will run off the rails in some unexpected way. .... 
I’ve long harboured doubts about the metric mania, but it’s all laid out in a new book, The Tyranny of Metrics, by Jerry Muller, a history professor at the Catholic University of America, in Washington DC....

Wednesday, May 2, 2018

Two things every Ph.D thesis should contain

I find that too often both of the elements below are missing or are superficial in a thesis. Yet doing them is important training for a student and just plain old good science.

Suggestions for Future Directions
A good research project will raise new questions and challenges.
Most projects do not get as far as the advisor and student would have liked.
The student should write about:
What would do if I had more time?
What should the next Ph.D. student do?
This can be a separate section or chapter at the end of the thesis.

A sober assessment of the strengths and weaknesses of the approach taken and the methods used.
In these current times of hype, the fierce competition for funding and publication in luxury journals mean that many are reluctant to admit any weakness or the value of possible alternatives.
During question time for a colloquium, the speaker was asked, "What are the weaknesses of your approach compared to the alternatives?"
"I can't think of any. It is better in every way."
However, the only way we can improve things is by considering the weaknesses of what we are doing.

Another reason why both of these may be neglected because doing them well is just plain old hard work.

I think these features are equally important in undergraduate and Masters theses as well.

What do you think?
Are there other essentials?