Condensed concepts

Previously, I highlighted the important but basic skill of being skeptical.  Here I expand on the idea. An experimental paper may make a claim, "We have observed interesting/exciting/exotic effect C in material A by measuring B." How do you critically assess such claims? Here are three issues to consider. It is as simple as ABC! 1. The material used in the experiment may not be pure A. Preparing pure samples, particularly "single" crystals of a specific material of know chemical composition is an art. Any sample will be slightly inhomogeneous and will contain some chemical impurities, defects, ... Furthermore, samples are prone to oxidation, surface reconstruction, interaction with water, ... A protein may not be in the native state... Even in a ultracold atom experiment one may have chemically pure A, but the actual density profile and temperature may not be what is thought. There are all sorts of checks one can do to characterise the structure and chemic

My wife and I went to see the movie, The Man Who Knew Infinity , which chronicles the relationship between the legendary mathematicians Srinivasa Ramanujan and G.H. Hardy . I knew little about the story or the maths and so learnt a lot. I think one thing it does particularly well is capturing the passion that many scientists and mathematicians have about their research, including both the beauty of the truth we discover and the rich enjoyment of the finding it. The movie obviously highlights the unique, weird, and intuitive way that Ramanujan was able surmise extremely complex formula without proof. I subsequently read a little more. There is a nice piece on The Conversation , praising the movie's portrayal of mathematics. A post on the American Mathematical Society blog  discusses the making of the movie including a discussion with the mathematician Ken Ono , who was a consultant. Stephen Wolfram also has a long blog post about Ramanujan. I enjoyed reading the 1993 artic

I recently met two people who got Ph.Ds from Australian universities who told me their stories. I found them disappointing. Dr. A had a very senior role in government. After his contract ended he spend one year writing a thesis, largely based on his experience, submitted it and was awarded a Ph.D. He is now a Professor at a (mediocre) private university directing a research centre on government policy. Dr. B was a software engineer. He worked part time and enrolled in a Ph.D in computer science. He would come on campus about once a month to meet his supervisor. As far as I am aware this was the only interaction he ever had with anyone from the university. He never went to any seminars, talked to other students, or took courses. I don't doubt that on some level the theses submitted by these students may be comparable to those of other students and "worthy" of a Ph.D. However, a colleague recently pointed out that at almost all universities the first page of the the

I used to find the concept of the chemical potential rather confusing. Hence, it is not surprising that students struggle too. I could say the mantra that "the chemical potential is the energy required to add an extra particle to the system" but how it then appeared in different thermodynamic identities and the Fermi-Dirac distribution always seemed a bit mysterious. However, when I first taught statistical mechanics 15 years ago I used the great text by Daniel Schroeder. He has a very nice discussion  that introduces the chemical potential. He considers the composite system shown below, where a moveable membrane connects two systems A and B. Energy and particles can be exchanged between A and B. The whole system is isolated by the environment and so the equilibrium state is the one which maximises the total entropy of whole system. Mechanical equilibrium (i.e. the membrane does not move) occurs if the pressure of A equals the pressure of B. Thermal equilibrium (i.e

There is some fascinating solid state physics in geology, particularly associated with phase transitions between different crystal structures under high pressure. This provides some interesting examples and problems when teaching undergraduate thermodynamics. One of many nice features of the text by Schroeder is that it has discussions and problems associated with these phase transitions. However, I would not have thought that the electronic transport properties, and particularly the role of electron correlations, would be that relevant to geophysics. But, I recently learnt this is not the case. A really basic unanswered question in geophysics is the origin and stability of the earths magnetic field due to the geodynamo . It turns out that the magnitude of the thermal conductivity of solid iron at high pressures and temperatures matters. One must consider not just the relative stability of different crystal structures but also the relative contributions of electron-phonon and electr

The world is changing rapidly. It is hard to keep up. Companies boom and bust overnight... Rush .. New technologies disrupt whole industries... Whoosh....  People continually change not just jobs but field....  Universities need to look out..... They need to change rapidly.... The web is totally transforming higher education... Tenure is outdated... Focus on the short term... You may not survive... Whoosh... This is a common narrative. But is it actually true? Late last year, The Economist had an interesting article "The Creed of Speed: Is business really getting quicker?" They look at certain objective quantitative measures to argue that the (surprising) answer to the question is no. It is worth reading the whole article, but here a few snippets. The graph below shows how little some measures have changed in the past 10 years. More creative destruction would seem to imply that firms are being created and destroyed at a greater rate. But the odds of a company dr

I love the phase diagram below and like to show it to students because it is so cute. However, in terms of understanding, I always found it a bit bamboozling. On monday I am giving a lecture on phase transformations of mixtures, closely following the nice  textbook by Schroeder , Section 5.4. Such a phase diagram is quite common. Below is the phase diagram for the liquid-solid transition in mixtures of tin and lead. Having prepared the lecture, I now understand the physical origin of these diagrams. Eutectic  [greek for easy melting] point is the lowest temperature at which the liquid is stable. What is amazing is that one can understand these diagrams from simple arguments based on a very simple and physically motivated functional form for the Gibbs free energy that includes the entropy of mixing. It is of the form G(x) = C + D x + E x(1-x) + T [xlnx + (1-x)ln(1-x)] where x is the mole fraction of the one substance in the mixture and T is the temperature.

Next month I am giving two versions of a talk, "Absence of a quantum limit to the shear viscosity in strongly interacting fermion fluids." The first talk will be a UQ Quantum science seminar and the second at the Telluride workshop on Condensed Phase Dynamics . These are quite different audiences, but both will not be so familiar with the topic and so I need good background slides to introduce and motivate the fascinating topic. The talk is largely based on a recent paper with Nandan Pakhira. Here is one of the slides I am working on. Some of the points I want to make here are the following. There is experimental data on real systems. This graph shows how for liquid 3He the shear viscosity varies by 3 orders of magnitude. Here the shear viscosity decreases with increasing temperature (while the mean-free path gets shorter). This is counter-intuitive, a feature shared by dilute classical gases. Fermi liquid behaviour is seen at low temperatures with the viscosit

How might you achieve some of the following desirable teaching goals? Get students to read the text book Find out what students are enjoying learning Find out what students are struggling to understand Keep students engaged Get feedback during the semester rather than at the end through student evaluations. A key component of innovative teaching approaches such as peer assisted instruction, flipped classrooms, and just in time learning (a la  Eric Mazur and Carl Wieman ) are getting students before each class meeting to complete a short online quiz, based on reading the relevant part of the text. Ideally the teacher looks at the students answers before the class to get a feel for where they are at in understand and to address specific issues in the class. Some of my UQ physics colleagues have really pursued this approach.  I am currently teaching a second year undergraduate thermodynamics class with Joel Corney , from whom I have learnt a lot about  teaching innovation. O

I recently spoke to a colleague who has now been teaching for three years. I asked her, "What have you learned from the experience? What would you do differently? What advice do you have for new faculty members?" Here is what she said. " I taught too slowly and did not cover enough material. Students complained about this. I assumed the students had weaker background knowledge than they did. I should have taught at a more advanced level. The exams I set were too easy and too many students got high grades. I should not have done so many worked examples in class. I should not have spent so much class time answering students questions. I followed the text book closely. It would have been better to challenge the students more by drawing material from a range of sources. " If you think this is surprising, it is because everything I wrote above is a lie. I have never heard anyone say anything like that! In fact, I always hear people say the exact opposite. Yet we

Five years ago, Antoine Georges and collaborators invoked the metaphor of the greek god Janus to represent the "two-faced" effects of Hund's coupling in strongly correlated metals. I wondered where they got this idea from: was it from someones rich classical education? In the  KITP talk , I recently watched online, Antoine mentioned he got the idea from Pierre de Gennes. In his 1991 Nobel Lecture , de Gennes said the Janus grains, first made by C. Casagrande and M. Veyssie. The god Janus had two faces. The grains have two sides: one apolar and the other polar. Thus they have certain features in common with surfactants. But there is an interesting difference if we consider the films which they make —for instance, at a water-air interface. A dense film of a conventional surfactant is quite impermeable. On the other hand, a dense film of Janus grains always has some interstices between the grains, and allows for chemical exchange between the two sides: "the skin

For some reason I have only become more aware of this issue recently. I have noticed, particularly among weaker undergraduate students, a lack of concern about details. This is not just among beginning undergrads but even final year students. Here are some examples, from a range of levels. Language. Force, energy, and power are not the same thing. Each refers to distinct physical concepts and entities. Similarly, temperature, heat, internal energy, and entropy... The wave function, potential energy, and probability.... Units. Every physical quantity has well-defined units. You need to state them and keep track of them in calculations. Significant figures. These need to be justified and self-consistent. Arguments and solutions to problems. These need to be stated in a logical order. Assumptions and approximations need to be stated and justified. The sloppiness is particularly evident in the exam papers of weaker students. One might excuse some because of the stress