Friday, September 20, 2019

Common examples of symmetry breaking

In his beautiful book, Lucifer's Legacy: The Meaning of Asymmetry, Frank Close gives several nice examples of symmetry breaking that make the concept more accessible to a popular audience.

One is shown in the video below. Consider a spherical drop of liquid that hits the flat surface of a liquid. Prior to impact, the system has continuous rotational symmetry about an axis normal to the plane of the liquid and through the centre of the drop. However, after impact, a structure emerges which does not have this continuous rotational symmetry, but rather a discrete rotational symmetry.

Another example that Close gives is illustrated below. Which napkin should a diner take? One on their left or right? Before anyone makes a choice there is no chirality in the system. However, if one diner chooses left others will follow, symmetry is broken and a spontaneous order emerges.

Thursday, August 29, 2019

My tentative answers to some big questions about CMP

In my last post, I asked a number of questions about Condensed Matter Physics (CMP) that my son asked me. On reflection, my title basic questions" was a misnomer, because these are actually rather profound questions. Also, it should be acknowledged that the answers are quite personal and subjective. Here are my current answers.

1. What do you think is the coolest or most exciting thing that CMP has discovered?

Superconductivity.

explained?

BCS theory of superconductivity.
Renormalisation group (RG) theory of critical exponents.

2. Scientific knowledge changes with time. Sometimes long-accepted facts''  and theories'' become overturned.  What ideas and results are you presenting that you are almost absolutely certain of?

Phase diagrams of pure substances.
Crystallography.
Landau theory and symmetry breaking as a means to understand almost all phase transitions.
RG theory.
Bloch's theorem and band theory as a framework to understand the electronic properties of crystals.
Quantisation of vortices.
Quantum Hall effects.
Emergence.

What might be overturned?

I will be almost certain of everything I will write about in the Very Short Introduction. This is because it centers around concepts and theories that have been able to explain a very wide swathe of experiments on diverse materials and that have been independently reproduced by many different groups.
I am deliberately avoiding describing speculative theories and the following.
Ideas, results, and theories based on experiments that did not involve the actual material claimed, involved significant curve fitting, or large computer simulations.
Many things published in luxury journals during the last twenty years.

3. What are the most interesting historical anecdotes?

These are so interesting and relevant to major discoveries that they are worth including in the VSI.
Graphene and sellotape.
Quasi-crystals.
Bardeen's conflict with Josephson.
Abrikosov leaving his vortex lattice theory in his desk drawer because Landau did not like it.

What are the most significant historical events?

Discovery of x-ray crystallography
Discovery of superconductivity.
Landau's 1937 paper.
BCS paper.
Wilson and Fisher.

Who were the major players?

They are so important that they are worthy of a short bio in the text.
Onnes.
Landau.
Bardeen.
Anderson.
Wilson.

4. What are the sexy questions that CMP might answer in the foreseeable future?

Is room-temperature superconductivity possible?

Friday, August 23, 2019

Basic questions about condensed matter

I am trying out draft chapters of Condensed matter physics: A very short introduction, on a few people who I see as representative of my target audience. My son is an economist but has not studied science beyond high school. He enjoys reading widely. He kindly agreed to give me feedback on each draft chapter. Last week he read the first two chapters and his feedback was extremely helpful. He asked me several excellent questions that he thought I should answer.

1. What do you think is the coolest or most exciting thing that CMP has discovered? explained?

2. Scientific knowledge changes with time. Sometimes long-accepted facts''  and theories'' become overturned? What ideas and results are you presenting that you are almost absolutely certain of? What might be overturned?

3. What are the most interesting historical anecdotes? What are the most significant historical events? Who were the major players?

4. What are the sexy questions that CMP might answer in the foreseeable future?

I have some preliminary answers. But, to avoid prejudicing some brainstorming, I will post later.
What answers would you give?

Tuesday, August 20, 2019

The global massification of universities

A recent issue of The Economist has an interesting article about the massive expansion in higher education, both private and public, in Africa.
The thing I found most surprising and interesting is the graphic below.

It compares the percentage of the population within 5 years of secondary school graduation are enrolled in higher education, in 2000 and 2017. In almost all parts of the world the percentage enrollment has doubled in just 17 years!
I knew there was rapid expansion in China and Africa, but did not realise it is such a global phenomenon.

Is this expansion good, bad, or neutral?
It is helpful to consider the iron triangle of access, cost, and quality. You cannot change one without changing at least one of the others.

I think that this expansion is based on parents, students, governments, and philanthropies holding the following implicit beliefs uncritically. Based on the history of universities until about the 1970s. Prior to that universities were fewer, smaller, more selective, had greater autonomy (both in governance, curriculum, and research).

1. Most students who graduated from elite institutions went on to successful/prosperous careers in business, government, education, ...

2. Research universities produced research that formed the foundation for amazing advances in technology and medicine, and gave profound new insights into the cosmos, from DNA to the Big Bang.

Caution: the first point does not imply that a university education was crucial to the graduates' success. Correlation and causality are not the same thing. The success of graduates may be just a matter of signaling.  Elite institutions carefully selected highly gifted and motivated individuals who were destined for success. The university just certified that the graduates were hard-working, smart, and conformist.''

But the key point is these two observations (beliefs) concern the past and not the present. Universities are different.  Massification and the stranglehold of neoliberalism (money, marketing, management, and metrics) mean that universities are fundamentally different, from the student experience to the nature of research.

According to Wikipedia,
Massification is a strategy that some luxury companies use in order to attain growth in the sales of product. Some luxury brands have taken and used the concept of massification to allow their brands to grow to accommodate a broader market.
What do you think?
Are these the key assumptions?
Will massification and neoliberalism undermine them?

Tuesday, August 13, 2019

J.R. Schieffer (1931-2019): quantum many-body theorist

Bob Schrieffer died last month, as reported in a New York Times obituary.

Obviously, Schrieffer's biggest scientific contribution was coming up with the variational wave-function for the BCS theory of superconductivity.
BCS theory was an incredible intellectual achievement on many levels. Many great theoretical physicists had failed to crack the problem. The elegance of the theory was manifest in the fact that it was analytically tractable, yet could give a quantitative description of diverse physical properties in a wide range of materials. BCS also showed the power of using quantum-field-theory techniques in solid state theory. This was a very new thing in the late 50s. Then there was the following cross-fertilisation with nuclear physics and particle physics (e.g. Nambu).

Another significant contribution was the two-page paper from 1966 that used a unitary transformation to connect the Kondo model Hamiltonian to that of the Anderson single impurity model. In particular, it gave a physical foundation for the Kondo model, which at the time was considered somewhat ad hoc.
John Wilkins wrote a nice commentary on the background history and significance of the Schrieffer-Wolff transformation.
The SW transformation is an example of a general strategy of finding an effective Hamiltonian for a reduced Hilbert space. This can also be done via quasi-degenerate perturbation theory. In different words, when one integrates out'' the charge degrees of freedom in the Anderson model one ends up with the Kondo model.

There is also the Su-Schrieffer-Heeger model, that is related to Heeger's Nobel Prize in Chemistry. However, although this spawned a whole industry (that I worked in as a postdoc with Wilkins) its originality and significance is arguably not comparable to BCS and SW.

Because of when he was born, like many of the pioneers of quantum many-body theory, Schrieffer may have been born for success?

I am somewhat (scientifically) descended from Schrieffer because I did a postdoc with John Wilkins, who was one of Schrieffer's first PhD students. My main interaction with Schrieffer was during 1995-2000. Each year I would visit my collaborator, Jim Brooks, at the National High Magnetic Field Laboratory, and would have some helpful discussions with Schrieffer. During one of those visits, I stumbled across a compendium of reprints from a Japanese lab. [This was back in the days when some people snail-mailed out such things to colleagues]. It had been sent to Schrieffer and contained a copy of a paper by Kino and Fukuyama on a Hubbard model for organic charge transfer salts. That was the starting point for my work on that topic.

Tuesday, August 6, 2019

What is the mass of a molecular vibration?

This is a basic question that I have been puzzling about. I welcome solutions.

Consider a diatomic molecule containing atoms with mass m1 and m2. It has a stretch vibration that can be described by a harmonic oscillator with a reduced mass mu given by
.
Now consider a polyatomic molecule containing N atoms.
It will have 3N-6 normal modes of vibration.
[The 6 is due to the fact that there are 6 zero-frequency modes: 3 rigid translations and 3 rotations of the whole molecule].
In the harmonic limit, the normal mode problem is solved below.
[I follow the classic text Wilson et al., Molecular Vibrations].
The problem is also solved in matrix form in Chapter 6 of Goldstein, Classical Mechanics].

One now has a collection of non-interacting harmonic oscillators. All have mass = 1. This is because the normal mode co-ordinates have units of length * sqrt(mass).

The quantum chemistry package Gaussian does more. It calculates a reduced mass mu_i for each normal mode i using the formula below.
This is discussed in these notes on the Gaussian web site. From mu_i and the normal mode frequency_i it then calculates the spring constant for each normal mode.

I have searched endlessly, and tried myself, but have not been able to answer the following basic questions:

1. How do you derive this expression for the reduced mass?
2. Is this reduced mass physical, i.e. a measurable quantity?

Similar issues must also arise with phonons in crystals.

Any recommendations?

Tuesday, July 23, 2019

Different approaches to popular science writing

Since I am working on a Very Short Introduction (VSI) to condensed matter physics I am looking at a lot of writing about science for popular audiences. I have noticed several distinct approaches that different authors take. They all have strengths and weaknesses.

Historical
The story of discoveries and the associated scientists is told. A beautiful example is A Short History of Nearly Everything by Bill Bryson.
When done well this approach has many positives. Stories can be fun and easy to read, particularly when they involve quirky personalities, serendipity, and fascinating anecdotes. Furthermore, this shows how hard and messy real science is, and that science is a verb, not just a noun. On the other hand, it can be a bit challenging for readers as they have to understand not just the successes but also why certain theories, experiments, and interpretations were wrong along the way.  Many writers also seem eager to burden readers will all sorts of historical background details about scientists, their families, and their local context. Sometimes these details are interesting. Other times they seem just boring fluff. Generally, most agree that one does not learn and understand a scientific subject best by learning its history. So why take this approach in popular writing?

Literary pleasure
People read novels and watch movies for pleasure. The goal is not necessarily to learn something (or a lot). I would put Brian Cox's writing and documentaries in this category. That is not a criticism. Rather than provide a lot of information I think the goal is more to induce awe, wonder, curiosity, and enjoyment.

Condensed textbook
Take an introductory text and cover all the same topics in the same order. Just cut out technical details and jargon. Lots of analogies are used to explain concepts. The obvious strength is the reader gets a good overview of the subject. The weakness is that this can be boring, involve defining a lot of terminology, and is actually too hard for the reader. One scary consequence is that some readers actually think they now actually understand the subject.

Hype
This comes in several forms. One is that the theory or topic of interest (whether complexity, quantum information, self-organised criticality, sociobiology, ....) is THE answer. It explains everything. The second form of hype is technological: this science is going to lead a new technology that will change the world. Generally, this fits the genre of science as salvation''.

Conceptual
An example is Laughlin's A Different Universe. A challenge is that this requires readers to like learning new concepts and have an ability to think abstractly.

Except for hype, I think all of these approaches have their merits. Ideally, one would like to incorporate elements of all of them.

What do you think? Are there other approaches?

Friday, June 28, 2019

The bloody delusions of silicon valley medicine

On a recent flight, I watched the HBO documentary The Inventor: Out for Blood in Silicon Valley. It chronicles the dramatic rise and fall of Elizabeth Holmes, founder of a start-up, Theranos, that claimed to have revolutionised blood testing.

There is a good article in the New Republic
What the Theranos Documentary Misses
Instead of examining Elizabeth Holmes’s personality, look at the people and systems that aided the company’s rise.

In spite of the weaknesses described in that article, the documentary made me think about a range of issues at the interface of science, technology, philosophy, and social justice.

The story underscores Kauzmann's maxim, people will often believe what they want to believe rather than what the evidence before them suggests they should believe.''

Truth matters. Eventually, we all bounce up against reality: scientific, technological, economic, legal, ...  It does not matter how much hype and BS one can get away, eventually, it will all come crashing down. It is just amazing that some people seem to get away with it for so long...
This is why transparency is so important. A bane of modern life is the proliferation of Non-Disclosure Agreements. Although, I concede they have a limited role is certain commercial situations, they seem to be now used to avoid transparency and accountability for all sorts of dubious practises in diverse social contexts.

The transition from scientific knowledge to a new technology is far from simple. A new commercial device needs to be scalable, reliable, affordable, and safe. For medicine, the bar is a lot higher than a phone app!

Theranos had a board featuring big'' names in politics, business, and military, such as Henry Kissinger, George Shulz, Daniel Mattis,.. All these old men were besotted with Holmes and more than happy to take large commissions for sitting on the board. Chemistry, engineering, and medical expertise were sorely lacking. However, even the old man with relevant knowledge Channing Robertson was a true believer until the very end.

Holmes styled herself on Steve Jobs and many wanted to believe that she would revolutionise blood testing. However, the analogy is flawed. Jobs basically took existing robust technology and repackaged and marketed it in clever ways. Holmes claimed to have invented a totally new technology. What she was trying to do was a bit like trying to build a Macintosh computer in the 1960s.

Wednesday, June 12, 2019

Macroscopic manifestations of crystal symmetry

In my view, the central question that Condensed Matter Physics (CMP) seeks to answer is:
How do the properties of a distinct phase in a material emerge from the interactions between the atoms of which the material is composed?
CMP aims to find a connection between the microscopic properties and macroscopic properties of a material. This requires determining three things: what the microscopic properties are, what the macroscopic properties are, and how the two are related. None of the three is particularly straightforward. Historically, the order of discovery is usually: macroscopic, microscopic, connection. Making the connection between microscopic and macroscopic can take decades, as exemplified in the BCS theory of superconductivity.

Arguably, the central concept to describe the macroscopic properties is broken symmetry, which can be quantified in terms of an order parameter. Connecting this microscopics is not obvious. For example, with superconductivity, the sequence of discovery was experiment, Ginzburg-Landau theory, BCS theory, and then Gorkov connected BCS and Ginzburg-Landau.

When we discuss (and teach about) crystals and their symmetry we tend to start with the microscopic, particularly with the mathematics of translational symmetry, Bravais lattices, crystal point groups, ...
Perhaps this is the best strategy from a pedagogical point of view in a physics course.
However, historically this is not the way our understanding developed.
Perhaps if I want to write a coherent introduction to CMP for a popular audience I should follow the historical trajectory. This can illustrate some of the key ideas and challenges of CMP.

So let's start with macroscopic crystals. One can find beautiful specimens that have very clean faces (facets).

Based on studies of quartz, Nicolas Steno in 1669 proposed that the angles between corresponding faces on crystals are the same for all specimens of the same mineral".  This is nicely illustrated in the figure below which looks at different cross-sections of a quartz crystal. The 120-degree angle suggests an underlying six-fold symmetry. This constancy of angles was formulated as a law by Romé de l'Isle in 1772.

Rene Just Hauy then observed that when he smashed crystals of calcite that the fragments always had the same form (types of facets) as the original crystal. This suggested some type of translational symmetry, i.e. that crystals were composed of some type of polyhedral unit. In other words, crystals involve a repeating pattern.

The mathematics of repeating units was then worked out by Bravais, Schoenflies, and others in the second half of the nineteenth century. In particular, they showed that if you combined translational symmetries and point group symmetries (rotations, reflections, inversion) that there were only a discrete number of possible repeat structures.

Given that at the beginning of the twentieth century, the atomic hypothesis was largely accepted, particularly by chemists, it was also considered reasonable that crystals were periodic arrays of atoms and molecules. However, we often forget that there was no definitive evidence for the actual existence of atoms. Some scientists such as Mach considered them a convenient fiction. This changed with Einstein's theory of Brownian motion (1905) and the associated experiments of Jean Perrin (1908). X-ray crystallography started in 1912 with Laue's experiment. Then there was no doubt that crystals were periodic arrays of atoms or molecules.

Finally, I want to mention two other macroscopic manifestations of crystal symmetry (or broken symmetry): chirality and distinct sound modes (elastic constants).

Louis Pasteur made two important related observations in 1848. All the crystals of sodium ammonium tartrate that he made could be divided into two classes: one class was the mirror image of the other class. Furthermore, when polarised light traveled through these two classes, the polarisation was rotated in opposite directions. This is chirality (left-handed versus right-handed) and means that reflection symmetry is broken in the crystals. The mirror image of one crystal cannot be superimposed on the original crystal image. The corresponding (trigonal) crystals for quartz are illustrated below.

Aside. Molecular chirality is very important in the pharmaceutical industry because most drugs are chiral and usually only one of the chiralities (enantiomers) is active.

Sound modes (and elasticity theory) for a crystal are also macroscopic manifestations of the breaking of translational and rotational symmetries. In an isotropic fluid, there are two distinct elastic constants and as a result, two distinct sound modes. Longitudinal and transverse sound have different speeds. In a cubic crystal, there are three distinct elastic constants and three distinct sound modes. In a triclinic crystal (which has no point group symmetry) there are 21 distinct elastic constants. Hence, if one measures all of the distinct sound modes in a crystal, one can gain significant information about which of the 32 crystal classes that crystal belongs too. (See Table A.8 here).

Aside: the acoustic modes in a crystal are the Goldstone bosons that result from the breaking of the symmetry of continuous and rotational translations of the liquid.

This post draws on material from the first chapter of Crystallography: A Very Short Introduction, by A.M. Glazer.

Friday, May 31, 2019

Max Weber on the evolution of institutions

Max Weber is one of the founders of sociology. This post is about two separate and interesting things I recently learned about him.

A while ago I discussed Different phases of growth and change in human organisations, based on a classic article from Harvard Business Review. [Which had no references or data!]
My friend Charles Ringma recently brought to my attention somewhat related ideas from Max Weber.
According to Wikipedia

Weber distinguished three ideal types of political leadership (alternatively referred to as three types of domination, legitimisation or authority):[52][111]
1. charismatic domination (familial and religious),
2. traditional domination (patriarchspatrimonialismfeudalism) and
3. legal domination (modern law and state, bureaucracy).[112]
In his view, every historical relation between rulers and ruled contained such elements and they can be analysed on the basis of this tripartite distinction.[113] He notes that the instability of charismatic authority forces it to "routinise" into a more structured form of authority.[79]

I also learnt that Weber had a long history of mental health problems. According to Wikipedia

In 1897 Max Weber Sr. died two months after a severe quarrel with his son that was never resolved.[7][37] After this, Weber became increasingly prone to depression, nervousness and insomnia, making it difficult for him to fulfill his duties as a professor.[17][26] His condition forced him to reduce his teaching and eventually leave his course unfinished in the autumn of 1899. After spending months in a sanatorium during the summer and autumn of 1900, Weber and his wife travelled to Italy at the end of the year and did not return to Heidelberg until April 1902. He would again withdraw from teaching in 1903 and not return to it till 1919. Weber's ordeal with mental illness was carefully described in a personal chronology that was destroyed by his wife. This chronicle was supposedly destroyed because Marianne Weber feared that Max Weber's work would be discredited by the Nazis if his experience with mental illness were widely known.[7][38]

This puts Weber in a similar class to many other distinguished scholars who had significant mental health problems: Boltzmann, John Nash, Drude, Michel Foucault, ...

Tuesday, May 28, 2019

Spin-crossover in geophysics

Most of my posts on spin-crossover materials have been concerned with organometallic compounds. However, this phenomena can also occur in inorganic materials. Furthermore, it may be particularly relevant in geophysics. A previous post discussed how strong electron correlations may play a role in geomagnetism and DMFT calculations have given some insight.

A nice short overview and introduction is
Electronic spin transition of iron in the Earth's deep mantle
Jung‐Fu Lin Steven D. Jacobsen Renata M. Wentzcovitch

[It contains the figure below]
The main material of interest is magnesiowüstite, an alloy of magnesium and iron oxide,
(Mg1xFex)O

Experimental studies and DFT calculations suggest that as the pressure increases the iron ions undergo a transition from high spin to low spin. The basic physics is that the pressure reduces the Fe-O bond lengths which increases the crystal field splitting.
In geophysics, the pressure increases as one goes further underground.

DFT+U calculations are reported in
Spin Transition in Magnesiowüstite in Earth’s Lower Mantle
Taku Tsuchiya, Renata M. Wentzcovitch, Cesar R. S. da Silva, and Stefano de Gironcoli

The main result is summarised in the figure below.
There is a smooth crossover from high spin to slow spin, as is observed experimentally. However, it should be pointed out that this smoothness (versus a first-order phase transition with hysteresis) is built into the calculation (i.e. assumed) since the low spin fraction n is calculated using a single site model.  On the other hand, the interaction between spins may be weak because this is a relatively dilute alloy of iron (x=0.1875).
Also, the vibrational entropy change associated with the transition is not included. In organometallics, this can have a significant quantitative effect on the transition.

The elastic constants undergo a significant change with the transition. This is important for geophysics because these changes affect phenomena such as the transmission of earthquakes.

Abnormal Elasticity of Single-Crystal Magnesiosiderite across the Spin Transition in Earth’s Lower Mantle
Suyu Fu, Jing Yang, and Jung-Fu Lin

A previous post considered changes in the elasticity and phonons in organometallic spin-crossover. Unfortunately, that work did not have the ability to resolve different elastic constants.

Friday, May 24, 2019

Is this an enlightened use of metrics?

Alternative title: An exciting alternative career for Ph.Ds in condensed matter theory!

There is a fascinating long article in The New York Times Magazine
How Data (and Some Breathtaking Soccer) Brought Liverpool to the Cusp of Glory
The club is finishing a phenomenal season — thanks in part to an unrivaled reliance on analytics.

This is in the tradition of Moneyball. Most of the data analytics team at Liverpool have physics Ph.Ds. It is led by Ian Graham who completed a Ph.D. on polymer theory at Cambridge.

On the one hand, I loved the article because my son and I are big Liverpool fans. We watch all the games, some in the middle of the night. On the other hand, I was a bit surprised that I liked the article since I am a strong critic of the use of metrics in most contexts, especially in the evaluation of scientists and institutions. However, I came to realise that, in many ways, what Liverpool is doing is not the blind use of metrics but rather using data as just one factor in making decisions.
Here are some of the reasons why this is so different from what now happens in universities.

1. The football manager (Jurgen Klopp, who has played and managed) is making the decisions, not someone who has never played or has had limited success with playing and managing (a board member or owner).

2. The data is just one factor in hiring decisions. For example, Klopp often spends a whole day with a possible new player to see what their personal chemistry is. Furthermore, he has watched them play (the equivalent of actually reading the papers of a scientist?).

3. A single metric (cf. goals scored, h-index, impact factor) is not being used to make a decision on who to recruit. Rather, many metrics are being used, to develop a complete picture. Furthermore, a major emphasis of the Moneyball approach is finding diamonds in the rough'', i.e. players who have unseen potential, because their unique gifts are being overlooked (because they are currently undervalued because they score poorly with conventional metrics) or they would be a potent combination with other current plays. The latter was a decision is recruiting Salah; the data suggested he would be a particularly powerful partner to Firmino. On the former, the article discusses in detail the analysis that led to Liverpool recruiting the Ghanian midfield,  Naby Keita.
Keita’s pass completion rate tends to be lower than that of some other elite midfielders. Graham’s figures, however, showed that Keita often tried passes that, if completed, would get the ball to a teammate in a position where he had a better than average chance of scoring. What scouts saw when they watched Keita was a versatile midfielder. What Graham saw on his laptop was a phenomenon. Here was someone continually working to move the ball into more advantageous positions, something even an attentive spectator probably wouldn’t notice unless told to look for it. Beginning in 2016, Graham recommended that Liverpool try to get him.

What might be an analogue of this approach in science?
A person who does not attract a lot of attention but has a record of writing papers that stimulate or are foundational to significant papers of better-known scientists?
A person who does very good science even though they have few resources?
A person who is particularly good at putting together collaborations?

Other suggestions?

Tuesday, May 21, 2019

Public talk on emergence

Every year in Australia there is a week of science outreach events in pubs, Pint of Science. I am giving a talk  tomorrow night, Emergence: from physics to sociology.
Here are the slides.

In the past, when explaining emergence I have liked to use the example of geometry. However, one can argue that a limitation of that case is there are not necessary many interacting components to the system. Hence, I think the example of language, discussed by Michael Polanyi is better.

Saturday, May 18, 2019

Phonons in organic molecular crystals.

In any crystal the elementary excitations of the lattice are phonons. The dispersion relation for these quasi-particles relates their energy and momentum. This dispersion relation determines thermodynamic properties such as the temperature dependence of the specific heat and plays a significant role in electron-phonon scattering and superconductivity in elemental superconductors. A nice introduction is in chapter 13 of Marder's excellent text. [The first two figures below are taken from there].

The dispersion relation is usually determined in at least one of three different ways.

1. The classical mechanics of balls and harmonic springs, representing atoms and chemical bonds, respectively. One introduces empirical parameters for the strengths of the bonds (spring constants).

2. First-principles electronic structure calculations, often based on density functional theory (DFT). This actually just determines the spring constants in the classical model.

3. Inelastic neutron scattering.

The figure below shows the dispersion relations for a diamond lattice using parameters relevant to silicon, using method 1. I find it impressive that this complexity is produced with only two parameters.

Furthermore, it produces most of the details seen in the dispersion determined by method 3. (Squares in the figure below.) which compare nicely with method 2. (solid lines below).

What about organic molecular crystals?
The following paper may be a benchmark.

Phonon dispersion in d8-naphthalene crystal at 6K
I Natkaniec, E L Bokhenkov, B Dorner, J Kalus, G A Mackenzie, G S Pawley, U Schmelzer and E F Sheka

The authors note that method 3. is particulary challenging for three reasons.
• The difficulties in growing suitable single-crystal samples.
• The high energy resolution necessary to observe the large number of dispersion curves (in principle there are 3NM modes, where N is the number of atoms per molecule and M is the number of molecules per unit cell).
• The high momentum resolution necessary to investigate the small Brillouin zone (due to the large dimensions of the unit cell).
The figure below shows their experimental data for the dispersions. The solid lines are just guides to the eye.

The authors also compare their results to method 1. However, the results are not that impressive, partly because it is much harder to parameterise the intermolecular forces, which are a mixture of van der Waals and pi-pi stacking interactions. Hence, crystal structure prediction is a major challenge.

A recent paper uses method 2. and compares the results of three different DFT exchange-correlation functionals to the neutron scattering data above.
Ab initio phonon dispersion in crystalline naphthalene using van der Waals density functionals
Florian Brown-Altvater, Tonatiuh Rangel, and Jeffrey B. Neaton

What I would really like to see is calculations and data for spin-crossover compounds.

Thursday, May 16, 2019

Introducing phase transitions to a layperson

I have written a first draft of a chapter introducing phase diagrams and phase transitions to a layperson. I welcome any comments and suggestions. Feel free to try it out on your aunt or uncle!

Tuesday, May 7, 2019

Fun facts about phonons

Today we just take it for granted that crystals are composed of periodic arrays of interacting atoms. However, that was only established definitively one hundred years ago.
I have been brushing up on phonons with Marder's nice textbook, Condensed Matter Physics.
There are two historical perspectives that I found particularly fascinating. Both involve Max Born.

In a solid the elastic constants completely define the speeds of sound (and the associated linear dispersion relationship). In a solid of cubic symmetry, there are only three independent elastic constants, C_11, C_44, and C_12.
Cauchy and Saint Venant showed that if all the atoms in a crystal interact through pair-wise central forces then C_44=C_12. However, in a wide range of elemental crystals, one finds that C_12 is 1-3 times larger than C_44. This discrepancy caused significant debate in the 19th century but was resolved in 1914 by Born who showed that angular forces between atoms could explain the violation of this identity. From a quantum chemical perspective, these angular forces arise because it costs energy to bend chemical bonds.

The first paper on the dynamics of a crystal lattice was by Born and von Karman in 1912. This preceded the famous x-ray diffraction experiment of von Laue that established the underlying crystal lattice. In 1965, Born reflected
The first paper by Karman and myself was published before Laue's discovery. We regarded the existence of lattices as evident not only because we knew the group theory of lattices as given by Schoenflies and Fedorov which explained the geometrical features of crystals, but also because a short time before Erwin Madelung in Göttingen had derived the first dynamical inference from lattice theory, a relation between the infra-red vibration frequency of a crystal and its elastic properties....
Von Laue's paper on X-ray diffraction which gave direct evidence of the lattice structure appeared between our first and second paper. Now it is remarkable that in our second paper there is also no reference to von Laue. I can explain this only by assuming that the concept of the lattice seemed to us so well established that we regarded von Laue's work as a welcome confirmation but not as a new and exciting discovery which it really was.
This raises interesting questions in the philosophy of science. How much direct evidence do you need before you believe something? I can think of two similar examples from more recent history: the observation of the Higgs boson and gravitational waves. Both were exciting, and rightly earned Nobel Prizes.
However, many of us were not particularly surprised.
The existence of the Higgs boson made sense because it was a necessary feature of the standard model, which can explain so much.
Gravitational waves were a logical consequence of Einstein's theory of general relativity, which had been confirmed in many different ways. Furthermore, gravitational waves were observed indirectly through the decay of the orbital period of binary pulsars.

Wednesday, May 1, 2019

Emergence: from physics to international relations

Today I am giving a seminar for the School of Political Science and International Studies at UQ.
Here are the slides.

Thursday, April 25, 2019

Modelling the emergence of political revolutions

When do revolutions happen? What are the necessary conditions?
Here are the claims of two influential political theorists.

a single spark can cause a prairie fire’’
Mao Tse Tung

“it is not always when things are going from bad to worse that revolutions break out,... On the contrary, it often happens that when a people that have put up with an oppressive rule over a long period without protest suddenly finds the government relaxing its pressure, it takes up arms against it. … liberalization is the most difficult of political arts”
Alexis de Tocqueville (1856)

Is it possible to test such claims? What is the relative importance of levels of perceived hardship and government illegitimacy, oppression, penalties for rebellion, police surveillance, ...?

An important paper in 2002 addressed these issues.
Modeling civil violence: An agent-based computational approach
Joshua M. Epstein

The associated simulation is available in NetLogo.
It exhibits a number of phenomena that can be argued to be emergent: they are a collective and are not necessarily unanticipated from the model.

Tipping points
There are parameter regimes at which there are no outbursts of rebellion.

Free assembly catalyzes rebellious outbursts
Epstein argues that this is only understood ex post facto.

Punctuated equilibrium
Periods of civil peace interspersed with outbursts of rebellion.

Probability distribution of waiting times between outbursts.
This distribution is not build explicitly into the model which involves only uniform probability distributions.
[Terminology here is analogous to biological evolution].

Salami corruption
Legitimacy can fall much further incrementally than it can in one jump, without stimulating large-scale rebellion.
[I presume the origin of Epstein's terminology is that salami is sliced something thinly... Maybe a clearer analogy would be the proverbial frog in a pot of slowly heated water].

de Tocqueville effect
Incremental reductions in repression can lead to large-scale rebellion. This is in contrast to incremental decreases in legitimacy.

Monday, April 22, 2019

Ten years of blogging!

I just realised that last month I had been blogging for ten years.
On the five year anniversary, I reflected on the influence that the blog has had on me.
I don't have much to add to those reflections. The second five years has not been as prolific but has been just as enriching and I am grateful for all the positive feedback and encouragement I have received from readers.

Wednesday, April 17, 2019

The emergence of social segregation

Individuals have many preferences. One is that we tend to like to associate with people who have some commonality with us. The commonality could involve hobbies, political views, language, age, wealth, ethnicity, religion, values, ... But some of us also enjoy a certain amount of diversity, at least in certain areas of life. We also have varying amounts of tolerance for difference.
A common social phenomenon is segregation: groups of people clump together in spatial regions (or internet connectivity) with those similar to them. Examples range from ethnic ghettos and teenage cliques to "echo chambers" on the internet.

The figure below shows ethnic/racist segregation in New York City. It is taken from here.

In 1971 Thomas Schelling published a landmark paper in the social sciences. It surprised many because it showed how small individual preferences for similarity can lead to large scale segregation. The context of his work was how in cities in the USA racially segregated neighbourhoods emerge.

One version of Schelling's model is the following. Take a square lattice and each lattice point can be black, white or vacant. Fix the relative densities of the three quantities and begin with a random initial distribution. A person is "unhappy" if only 2 or less of their 8 neighbours (nearest and next-nearest neighbours) on the lattice are like them. [They have a 25% threshold for moving]. They then move to a nearby vacancy. After many iterations/moves to an equilibrium is reached where everyone is "happy" but there is significant segregation.

The figure is taken from here.

There are several variants of the model that Schellman presented in later papers and an influential book Micromotives and Macrobehavior, published in 1978. He received the Nobel Prize in Economics in 2005 for work in game theory.

There is a nice simulation of the model in NetLogo. For example, you can see how if you set the individual preference for similarity at 30% one ends up with a local similarity of 70%.
In the Coursera, Model Thinking, Scott Page has a helpful lecture about the model.

This can be considered to be the first agent-based model. It is fascinating that Schellman did not use a computer but rather did his simulation'' manually on a checkerboard!

Physicists have considered variants of Schelling's model that can be connected to more familiar lattice models from statistical mechanics, particularly the Ising model. Examples include

Ising, Schelling and self-organising segregation
D. Stauffer and S. Solomon

Phase diagram of a Schelling segregation model
This connects to classical spin-1 models such as the Blume-Capel model.

A unified framework for Schelling's model of segregation
Tim Rogers and Alan J McKane

Competition between collective and individual dynamics
Sébastian Grauwin, Eric Bertin, Rémi Lemoy, and Pablo Jensen

Shelling's model is a nice example of emergence in a social system. A new entity [highly segregated neighbourhoods] emerges in the whole system thatwase not anticipated based on a knowledge of the properties of the components of the system.

Friday, April 12, 2019

Should graduate students pick their own research field?

Paul Romer won the Nobel Prize in Economics in 2018. There is an interesting podcast where he is in conversation with Tyler Cowan. In it, there is the following quote that readers may love!
We subsidize graduate education through money that goes to professors, but we let the professors make the decisions about the problems they work on, and then, therefore, the things the students are trained in. I’d rather let the students be the ones who decide, “Yeah, I don’t really want to work in high-energy physics. It’s kind of dead end. I think there’s something much more exciting in condensed-matter physics.”
I mostly post this for amusement.
[I thank my economist son, for bringing it to my attention].

However, Romer does raise an interesting issue. There is a distinct contrast between the systems in the USA and Australia. In the USA faculty get grants and use them to hire graduate students. In Australia, most Ph.D. students get their own scholarship (fellowship) which pays their tuition and a living allowance (salary). They are then free to pick an advisor (supervisor) and topic, which is then approved (usually routinely) by various committees.
I am not sure this is a better system. Too often, students still tend to flock to advisors who are "famous" (but give them little time or exploit them) or those working on the latest fashionable (hyped up) topic ... On the other hand, if a student wants to work on a particular topic that is currently not "hot" there is more opportunity for that, for better or worse.

What do you think?

Tuesday, April 9, 2019

Coupling of the lattice to spin-crossover transitions

There is a very nice paper
Complete Set of Elastic Moduli of a Spin-Crossover Solid: Spin-State Dependence and Mechanical Actuation
Mirko Mikolasek, Maria D. Manrique-Juarez, Helena J. Shepherd, Karl Ridier, Sylvain Rat, Victoria Shalabaeva, Alin-Ciprian Bas, Ines E. Collings, Fabrice Mathieu, Jean Cacheux, Thierry Leichle, Liviu Nicu, William Nicolazzi, Lionel Salmon, Gábor Molnár, and Azzedine Bousseksou

It investigates the spin-crossover in a specific compound with a suite of techniques, including x-ray diffraction, inelastic neutron scattering, and micro-electromechanical systems (MEMS).

The nice results reflect significant advances over the past few decades in neutron scattering and microfabrication.

The graph below shows the vibrational density of states of the Fe nuclei and the low-spin (LS) and high-spin (HS) states. Note how the LS modes around 50 meV (400 cm-1) soften significantly in the HS state. These modes are the Fe-N stretches in the octahedron. This softening is associated with a significant increase in entropy which helps drive the spin-crossover transition.
Note that there is a small parabolic part at low energies of a few meV.

The figure below is a "blow up" of the low energy data.
The energy resolution is amazing!
The graph shows the density of states divided by E^2.
Why?
In an isotropic solid (or a powder such as used here) in the Debye model for phonons, the density of states is proportional to E^2 and the proportionality is determined by the speed of sound, v_D.

One clearly sees several things.
1. For E less than about 3 meV, the DOS is quadratic in E, as predicted by Debye.
2. The lattice softens with the spin-crossover.
3. The deviation from quadratic occurs at a smaller E for HS than LS.

The values of the speed of sound can be combined with the lattice constant to estimate the Debye frequency, which is roughly where the deviation from quadratic dependence should occur.
I have done this (since the authors don't appear to have) and one gets values of the order of a few meV, consistent with experiment.

From the speed of sound, one can also determine the Young's modulus. This can then be compared to the bulk modulus, which can be determined from MEMS. The values obtained by these different methods are consistent with one another.
Overall, the values of the bulk modulus for different spin-crossover complexes, of order 5-10 GPa, are comparable to those for organic molecular crystals.

Friday, April 5, 2019

What is condensed matter physics?

How would you answer this question if you were asked by a non-expert who likes to learn and understand new things?
For example, a smart high school student, your uncle who reads a lot of popular science, an academic colleague in sociology, an economics graduate, ...
A draft of my answer is here.
I welcome suggestions for improvements.
Feel free to try it out on people you know who might be interested.

Tuesday, April 2, 2019

Chemistry finally joins the arxiv era

The physics arXiv started way back in 1991. Yet chemists strongly resisted following suit. Indeed if you posted a preprint on the arXiv American Chemical Society (ACS) journals would not publish it.
Eight years ago, Derek Lowe, asked Why Isn't There an arXiv for chemistry?

Well, finally ACS has succumbed and set up their own chemrxiv and announced that they will consider manuscripts that have been posted on the arXiv.

I thank Ben Powell for letting me know about the promising development.

Thursday, March 28, 2019

Why is hype bad?

There is no doubt that the level of hype in science is increasing. You see it in grant applications, university press releases, introductions and conclusion in papers (especially in luxury journals), talks, ... Hype is also a broader problem in society, including in the business world and politics.

Why is hype bad for science?
Some will say something like, I agree that it is not good, but we have to do it to survive. Anyway, we all know what is really true and so it does not matter..."

However, I think there are many problems, particularly for the long term flourishing of science.

Waste of time
Figuring out that a hyped'' result or research field is actually just hype can take significant time. This is particularly true if one actually tries to reproduce a result and discover all the problems.

Mis-allocation of resources
Researchers, students, and funding agencies flock to hyped fields. However, it can take quite a while and a lot of money for the community to come to the consensus that things are not going to live up to the hype. This is compounded by the fact that people whose careers are enhanced by a hyped result or field are not going to back down too easily and are going to want to keep things going, at least until the next big thing comes along.

Obscuring or hiding problems that need to be solved to make real progress
Making real and significant progress in science is very hard. Every technique has its limitations. Every result involves some uncertainty. Turning science in the lab into a commercially viable technology may arguably be even harder. The obstacles are many. The best way to progress in science and technology is to clearly and honestly state the problems and challenges. This is one of my many concerns about functional electronic materials.

Intellectual integrity
Science is all about intellectual integrity. Losing our credibility with broader society won't be good for science or for society, particularly when it comes to developing well-informed public policy.

Tuesday, March 26, 2019

Noel Hush (1924- 2019): pioneering theoretical chemist

I was sad to hear last week that Professor Noel Hush died at age 94. Noel [also known as Prof.] was a pioneer in theoretical chemistry and chemical physics. He had a profound influence on both fields, particularly in their development in Australia.

Arguably his greatest scientific contribution was in the theory of electron transfer. Depending on where you are from this is called Hush-Marcus theory, Marcus-Hush theory, or Marcus theory. In particular, in 1958 Hush derived one of the most important equations in chemical physics, which can be used for design principles for functional electronic materials. A key concept here is the notion of diabatic states.

I had the privilege of knowing and working with Prof. Hush on and off over the past decade. As I made an adiabatic transition from condensed matter into chemical physics Prof. Hush provided a lot of encouragement, wisdom, perspective, and ideas. He strongly believed that theoretical chemists and condensed matter theorists could have mutually beneficial interactions. Together with Jeff Reimers and Laura McKemmish, we co-authored seven papers together. The last papers were published when Noel was 90 years old!

Besides his significant legacy of scientific knowledge, there is an incredible legacy of people that he taught, supervised, mentored, encouraged, and collaborated with.

There is an interesting interview of Prof. Hush about his life by Robyn Williams from 2011.

Saturday, March 23, 2019

Emergence and complexity in social systems

Emergent phenomena occur in social systems. For example, self-organisation, power laws, networks, aggregation/segregation, political polarisation, political revolutions...
Can lessons from condensed matter physics help at all in understanding and modeling of social systems? Can analogies from social systems help non-scientists understand some of the basic ideas in condensed matter?

In two months I am giving a  seminar in a new UQ multi-disciplinary seminar series, Futures of International Order. In preparation, I am slowly engaging with relevant literature, particularly the work of Scott Page, including his course on Model Thinking at Coursera. The NetLogo software is helpful for exploring a range of simple models.
However, before plunging in here are a few tentative thoughts of ideas that might connect with condensed matter, in the vein of reviews such as

Physics and financial economics (1776–2014): puzzles, Ising and agent-based models
Didier Sornette

Statistical physics of social dynamics
Claudio Castellano, Santo Fortunato, and Vittorio Loreto

Emergence occurs in systems with many interacting components. In social systems, the components are human agents. They can aggregate into emergent entities such as neighbourhoods, institutions, and communities. Associated with these new entities are new scales of size (number of agents), length, time, and connectivity. New effective interactions between entities can also emerge. Even knowing all the details of the system components and the interactions it can be very difficult to predict the properties of the whole system. Surprises are common. Humility is needed.

Qualitative changes can occur due to small quantitative changes in a system parameter.
In condensed matter examples are phase transitions between different states of matter.  Furthermore, these changes can be directly seen as discontinuities or singularities in observables. Order parameters can quantify the changes. In social systems, similar phenomena are sometimes called tipping points.

Universality versus particularity
Close to a critical point for a phase transition most of the details of the system components and their interactions do not matter. Properties such as critical exponents are independent of most details. This is wonderful for theory because one can describe large classes of diverse systems with the same model/theory and one does not have to know all the details of the system.
Similar issues of universality are also relevant when one considers phenomena at different length scales. For example, one does not need to know anything about the atoms (even their existence!) in a crystal to develop a theory of elasticity or the propagation of sound waves.
When it comes to social systems there are a wide range of phenomena that can be potentially described by the same model. For example, Miller and Page point out that the essence of the standing ovation problem is how a binary choice (sit or stand) is influenced by the behaviour of one's neighbours. This is similar to choices as to whether to join a riot, take illegal drugs, or whether to vote of political party A or B.

Thursday, March 21, 2019

Mental health in academia

Even though I have not posted about it for a while, mental health continues to be on my radar. I monitor my own mental health carefully and generally things are going well. Tragically, I still meet many in academia struggling with the issue. It is also in the news because of the recent death by suicide of Princeton economist, Alan Krueger. A few months ago, Stanford theoretical physicist, Shoucheng Zhang, also died by suicide.

The Chronicle of Higher Education has an article about how Krueger's death is prompting conversations about how the culture of academia can be unconducive to mental health.

Last week there was an excellent New York Times Opinion piece by Lisa Pryor
Mental Illness Isn’t All in Your Head
A “formulation” gathers the biological, psychological and social factors that lead to a mental illness — and offers clues to the way out of suffering.

Tuesday, March 19, 2019

Alejandro Mezio and I just posted a preprint
Orbital-selective bad metals due to Hund’s rule and orbital anisotropy: a finite-temperature slave-spin treatment of the two-band Hubbard model

The central result is shown in the Figure below. It shows the phase diagram of the metallic phase as a function of temperature and the Hund's rule interaction J in a system with two bands of differing bandwidth. Uc1 ~ W1 is the critical interaction for a Mott insulator in a one band system with bandwidth W1.
The system is a Hund's metal in that the strong correlations arise from J and not from proximity to a Mott insulating phase (note that U=0.5Uc1).
In the orbital-selective bad metal, one of the bands is a coherent Fermi liquid (with well-defined Fermi surface) and the second (narrower) band is a bad metal.

Two things that I find particularly interesting are the following.

Stability of the bad metal and the orbital-selective bad metal are enhanced by increasing J and/or by increasing band anisotropy.

The temperatures at which the bad metals occur is orders of magnitude smaller than the Fermi temperature for the corresponding non-interacting system (being of the order of W1~ Uc1).

Thursday, March 14, 2019

Imaging orbital-selective quasi-particles in a Hund's metal

Over the past two decades, a powerful new technique has been developed to determine quasi-particle properties in strongly correlated electron systems, based on STM (scanning tunneling microscope) measurements. Quasi-particle interference (QPI) has proved to be particularly useful for studying cuprates (e.g. in revealing the d-wave pairing) and now for iron-based superconductors. The basic physics is as follows. One measures the changes in the local tunneling density of states N(r,E), associated with a single impurity that scatters quasi-particles with a change in momentum q. Then the Fourier transform of this change is

The text above is taken from a nice paper
Imaging orbital-selective quasiparticles in the Hund’s metal state of FeSe
A. Kostin, P.O. Sprau, A. Kreisel, Yi Xue Chong, A.E. Böhmer, P.C. Canfield, P.J. Hirschfeld, B.M. Andersen and J.C. Séamus Davis

They show theoretically that the intensity of the interference pattern is quite sensitive to the quasi-particle weights of the different d-orbital bands. The experiments are consistent with
The key figure is below. It shows shaded intensity plots of the change in DOS as a function of wavevector. The central column is experimental data with E increasing from -20 meV to +15 meV as one goes down the column. The left and right columns show theoretical values for the same quantities, calculated with all the quasi-particle weights Z=1 (left) and the Z values above (right).

The large variation between the Z values for different orbitals shows how the effect of the correlations are orbital selective.

The same Z values were used by the same cast of characters in a study of the superconducting state that showed orbital selectivity played a key role in the Cooper pairing, including the significant variation of the energy gaps over the different Fermi surfaces. The quantitative agreement between experiment and the associated theory is quite impressive.

I thank Alejandro Mezio for bringing the papers to my attention.

Thursday, March 7, 2019

Why is quantum matter so interesting?

Last year Ben Powell wrote a Perspective for Science, The Expanding Materials Multiverse. It begins with a nice statement about why quantum condensed matter is so interesting, exciting, and challenging.
High-energy physicists are limited to studying a single vacuum and its excitations, the particles of the standard model. For condensed-matter physicists, every new phase of matter brings a new “‘vacuum.” Remarkably, the low-energy excitations of these new vacua can be very different from the individual electrons, protons, and neutrons that constitute the material. The materials multiverse contains universes where the particle-like excitations carry only a fraction of the elementary electronic charge, are magnetic monopoles, or are their own antiparticles. None of these properties have ever been observed in the particles found in free space. Often, emergent gauge fields accompany these “fractionalized” particles, just as electromagnetic gauge fields accompany charged particles. On page 1101 of this issue, Hassan et al. provide a glimpse of the emergent behaviors of a putative new phase of matter, the dipole liquid. What particles live in this universe, and what new physics is found in this and neighboring parts of the multiverse?
There is also a nice figure which makes an everyday analogy to illustrate different states of matter.