Condensed concepts

A recent b ook  Dynamical heterogeneities in glasses, colloids, and granular media   contains a fascinating chapter where four experts [Jorge Kurchan, James Langer, Thomas Witten, and Peter Wolynes] give their answers to the questions below. I think we need more of these kind of frank discussions about scientific topics. I am slowly working through the answers. The most fascinating bit so far is Peter Wolynes inspiring response to Q9, including "I believe a young physicist who wants to work on any challenging problem in physics will eventually have to learn about glasses ." Q1) In your view, what are the most important aspects of the experimental data on the glass transition that any consistent theory explain? Is dynamical heterogeneity one of these core aspects?    Q2) Why should we expect anything universal in the behavior of glass-forming liquids? Is the glass-transition problem well defined?    Q3) In spin-glasses, the existence of a true spin-glass phase transiti

Last week I had a phone call from a journalist Andrew Grant at Science News, asking about quasi-particles. Why are they interesting? 1. Quasi-particles exist. It is not at all obvious why they should exist in strongly interacting quantum systems. Yet they are rather robust and found in diverse systems, ranging from atomic nuclei, to magnets, to metals, to neutron stars… Thus, they are an important organising principle in quantum many-body physics. 2. Occasionally quasi-particles have different quantum numbers to the constituent particles of a system. The most striking example is the fractional charge and statistics of quasi-particles in the fractional quantum Hall effect. 3. Many electronic materials of current interest [e.g. high-temperature superconductors] are “bad metals” that do not seem to have quasi-particles [except at low temperatures]. I find all of these are profound and surprising. They illustrate emergence.

Francis Su is a mathematics Professor at Harvey Mudd College. He is teaches a course in Real Analysis, the lectures of which you can watch on Youtube.  Last year he received the Haimo award from the Mathematical Association of America for excellence in teaching. In receiving the award he gave a deeply personal talk The Lesson of Grace in Teaching : From weakness to wholeness, the struggle and the hope I actually wanted to post about his talk when I first read it months ago, but was hesitant to because I feel I struggle so much with the issues he talks about. Finally posting it was prompted by two events. I got my latest student teaching evaluations and they were pretty good [more on that later]. (Sadly, this also illustrates how I am struggling with what Su is talking about: performance based identity). A friend is taking a course on teaching and he told me they had a whole session discussing clarification of personal values and how they shape your own teaching philos

Over the past few years I have advocated a simple diabatic state model to describe hydrogen bonding in a diverse range of molecular complexes. In my first paper I suggested the following parameterisation of the matrix element coupling the two diabatic states with two free parameters Delta1 and b, which describe the energy scale and length scale for the interaction. R1 is just a reference distance ~ 2.4 A, introduced so that the prefactor Delta1 corresponds to a physically relevant scale. The two parameter values I chose give a quantitative description of a wide range of properties [bond lengths, vibrational frequencies, and the associated isotope effects, when the quantum nuclear motion is taken into account. Last week I found this nice paper Solvent-Induced Red-Shifts for the Proton Stretch Vibrational Frequency in a Hydrogen-Bonded Complex. 1. A Valence Bond-Based Theoretical Approach  Philip M. Kiefer, Ehud Pines, Dina Pines, and James T. Hynes It uses a similar two-di

For my latest celebrity scientist speaking gig [at a small church youth group] my glamorous assistant [my wife] found a new demonstration to add to my repertoire,  Elephants toothpaste . It is described in this  Journal of Chemical Education paper . Hydrogen peroxide is thermodynamically unstable. However, you can buy bottles of it and they will remain useful for months. It will slowly decompose into water and oxygen. 2  H 2 O 2  → 2  H 2 O  +  O 2 However, if you add some iron chloride it acts as a catalyst and increases the decomposition rate by a factor of a thousand. You will see some amount of "bubbling" due to the oxygen gas produced. If blood [which contains haemoglobin] is added the rate increases by a factor of a million. Even better, if you add the enzyme catalase , the rate increases by a factor of a billion . In the demonstration the catalase is present in the yeast that is added. Catalase is one of the fastest catalysts known. It performs an incredibly impo

Why are they important? Why should you join? not join? Why are the membership numbers of some societies declining (some dramatically)? It seems every month the American Chemical Society (ACS) sends me a letter asking me to join. I am not sure who recommended me for membership. I find it ironic because I once tried to join the Royal Australian Chemical Institute but was rejected because they did not seem to think I was a real chemist. [ouch!] Over the years I have belonged to several societies. But, some of these memberships have lapsed. Recently, I was personally asked by one, "What do we have to do to get you to rejoin?" I did not have an answer, stimulating this post. First, let me say why these societies can be incredibly important . They can Publish good journals that are owned and run by scientists. These can avoid the problems of commercial outfits such as Nature [sensationalism over substance] and Elsevier [quantity over quality, dubious business practises].

In the mid-1990s, through the influence of Jim Brooks , I became interested in organic charge transfer salts. I read a very helpful paper by Kino and Fukuyama that considered a Hubbard model for the family kappa-(BEDT-TTF)2X. This led to me writing a review article and a short piece in Science , comparing the organics to the cuprates. Aside: Being young and naive, and living before impact factor obsessions, I made the mistake of publishing the review in Comments on Condensed Matter ,  which is not even listed on ISI Web of Science. I chose that journal because I knew it had published an influential review on heavy fermions by the stellar cast of Lee, Rice, Serene, Sham, and Wilkins. Fortunately, I put the paper on the arXiv and a lot of people read it, and the Science paper often gets cited, by association. The review stimulated a lot of work, particularly on the Hubbard model on the anisotropic triangular lattice at half filling, and the associated Heisenberg model for the Mott

At the American Chemical Society meeting last week J.T. Hynes gave a talk Some modest proposals for 21st century physical chemists  Here are his three main points. (1) The most familiar problems/phenomena may in fact not be at all already understood, and can provide fertile areas for discovery; (2) Just an experiment or a theory because it is 'old' (e.g. of a certain vintage) does not mean it is inferior/wrong despite the lack of novelty and modernity; (3) Simple, well-constructed analytic models have a significant role to play in comprehending and advancing both theory and experiment. Unfortunately, I was not at the meeting, but my colleague Seth Olsen  was and told me I would have enjoyed the talk. These points certainly resonate with my own views.

Movies sometimes feature gratuitous graphic violence and sex. Scientific papers sometimes feature gratuitous graphs. Before desktop computers it was a lot of work to produce a single graph. Now one can produce ten graphs in an afternoon! Why not put them all in the paper? The paper will be longer and give the impression of being more comprehensive. I feel that some students want to show all their graphs to show just how productive they have been. No! Not every graph you make should be in the paper. Analysis, synthesis, and discipline is needed. Figures should carry the weight of the paper. Many people, myself included, will scan the figures looking for something potentially interesting and important, in order to make a decision as to whether or not to actually read the paper. Figures and their captions need to be clear, comprehensible, and have significant content. Graphs should be like text: polished and repolished. Good authors work hard at writing, editing, polishin

Unfortunately, this past two months has seen the tragic death by suicide of Robin Williams,   Seth Teller [an MIT Computer Science Professor], and Yoshiki Sasai [co-author of two retracted Nature papers]. I thought the following video on depression was helpful.

A science fiction fantasy is that we should be able to make "materials by design" that have any physical property (density, thermal conductivity, hardness, thermoelectric figure of merit, heat capacity...)  that we desire. However, it seems that there are certain physical constraints that determine the overall scale of many physical properties. I find it helpful to have a feel for typical orders of magnitude. What is particularly interesting is that sometimes these magnitudes are related to fundamental constants [electronic charge (e), Boltzmann's constant (k_B), Planck's constant (hbar)] and basic length scales such as the lattice constant a of a crystal. Here are three scales I have emphasised before Resistivity ~ hbar a / e^2 ~ 100 microohm-cm  which is associated with the Mott-Ioffe-Regel limit. Thermoelectric power,  S ~ k_B/e ~ 86 microvolt/K Mobility, mu ~ e a^2/ hbar ~ 1 cm^2 V/sec One can find these scales by dimensional analysis or by doing thing

There is a very disturbing article in the New York Times about sexual harassment and discrimination of female scientists and science writers.

There is a very interesting paper The mechanism of proton conduction in phosphoric acid Linas Vilčiauskas, Mark E. Tuckerman, Gabriel Bester, Stephen J. Paddison, Klaus-Dieter Kreuer There are several reasons why neat liquid phosphoric acid (H3PO4) is such an interesting system the highest intrinsic proton conductivity of any known substance and is  σ  ≈ 0.15 S cm −1  above  T melt  = 42 °C.   This is like the conductivity of a bad metal but orders of magnitude larger than that of neat water. hydrogen bonded phosphates are ubiquitous in bimolecular systems and often involved in proton transport hydrogen bonded phosphates are electrolytes in high-temperature polymer electrolyte membrane fuel cells hydrogen bonded phosphates feature in many ferroelectric materials short intermolecular hydrogen bonds (the oxygen atom separation, R_OO ≈ 2.60 Å, compared to R_OO ≈ 2.85 Å in liquid water) it has a high dielectric constant (61), comparable to that of liquid water, but in the ga

Here is a helpful graphic that summarises the statistics of the employment trajectories of people who start doing a Ph.D in biology in the USA. I guess that the percentages are similar for physics and chemistry. Does anyone know the actual numbers? I welcome comment and critique on the numbers.

Previously I posted about the challenge of understanding the colossal thermoelectric effect in FeSb2 and the puzzles of the classic Kondo insulator FeSi. I talked about the former yesterday at the cake meeting [take 7 minutes to convince everyone they should read a particular paper]. I noticed for the first time just how large the thermal conductivity is, actually comparable to diamond at low temperatures. The red curve is FeSb2 and the black curve FeAs2, which is less correlated. This is of interest for at least two reasons. 1. The large thermal conductivity is bad for thermoelectric applications as it will significantly reduce the thermoelectric figure of merit. 2. It needs to be explained theoretically, including the large difference between FeSb2 and FeAs2. [Presumably the phonons are similar in the two compounds]. 3?. Does this make reliable thermoelectric measurements harder or easier? For comparison below I show the temperature dependence of the  thermal conduct

KISS = Keep It Simple, Stupid! "Make things as simple as possible, but no simpler." paraphrase of Einstein, for the real quote and its evolution, see here. A "principal object of theoretical research ... is to find the point of view from which the subject appears in its greatest simplicity." - J. W. Gibbs This post is a mixture of rant, observation, and exhortation. It is not just about theoretical model building but all of life! I also value simplicity in language, communication of ideas, administrative procedures, personal finances, software, email lists, meeting schedules, BibTex (arghh!), TV remote controls, .... But it seems that when it comes to things like grant applications , course profiles , .... there is a drive for greater complexity... The bigger the better. The more parameters the better... I sometimes wonder if the value I place on simplicity is just a personality trait or preoccupation.  Or  is there some universal value that is being l

Generally it is a lot easier to numerical calculations in imaginary time than in real time. A Fourier transform then gives the value of correlation functions at Matsubara frequencies . It then becomes a challenge to analytically continue to real frequencies. For results with little numerical noise the most widely used method is Pade approximants , as introduced by Vidberg and Serene . For results with statistical noise (e.g. from a quantum Monte Carlo simulation) a common approach is to use Maximum entropy methods, as reviewed by Jarrell and Gubernatis. In a Fermi liquid the quasi-particle weight Z is related to the real part of the self energy Sigma'(omega) by How does one get this from the self energy at imaginary frequencies i omega_n? It turns out one does not have to do the analytic continuation. There is an exact identity one can use, as described in this paper , by Arsenault, Semon, and Tremblay. [Minor correction: the Sigma in the middle of (12) should be Sigma&

The Stokes-Einstein equation relates the diffusion constant D of a macroscopic particle of radius r undergoing a Brownian motion to the viscosity eta of the fluid in which it is immersed. It is a beautiful and simple example of a fluctuation-dissipation relation. But suppose now we think about one of the individual atoms or molecules in the fluid. It also undergoes Brownian motion and one can define a self-diffusion constant. It is amazing to me that the Stokes-Einstein relation still holds for a wide range of liquids, temperatures, and pressures with r being of the order of the molecular radius. The figure and table below are taken from this paper. Can this relation be derived from microscopic theory? Zwanzig gave a heuristic justification here. Rah and Eu gave a derivation from stat. mech.  here. The Stokes-Einstein relation does break down as one approaches the glass temperature in a supercooled liquid, as for example shown here.  The origin of that breakdown is

Michelle Francl has a stimulating piece Take a number: Back-of-the-envelope calculations are an important part of chemistry  in Nature Chemistry. Francl asks her students, "Estimate the circumference of a benzene ring in metres". This is an example of a  Fermi problem. Previously I posted about the importance of teaching solid state physics in a way that helps students get a feel for orders of magnitude. I don't think I could write a comparable post for physical chemistry. This is partly my lack of expertise and experience, but also I suspect that things in chemistry are not as clear. [One day I hope I will get asked to teach a course.] For example, one thing I learnt and need to understand is that X-H bonds are shorter than X-X bonds. Indeed, Francl says I recently asked a few hundred of my closest chemical friends on Twitter and Facebook what should go on such a sheet for chemists, what they might encourage students to master. Schematics of periodic trends

Getting papers published can be a slow, inefficient, and frustrating process. For what it worth here is the strategy and associated rationale that I have generally evolved over the years. My primary goals are: engage relevant people with what I am doing get constructive feedback on the paper and the science get the paper published as smoothly and quickly as possible. Here are my usual steps: 1. get a local colleague to read the paper for feedback 2. put the paper on the arXiv [and write a post about it on this blog]. 3. send the preprint to a few people who might be referees or be able to provide useful feedback 4. revise the paper in response to feedback, including another proof read 5. submit the paper to a journal, sometimes suggesting people who have provided positive feedback already as possible referees. A few comments and rationale. My target journals are mostly Physical Review B and Journal of Chemical Physics. About once a year I send something to P