Condensed concepts

This post was stimulated by attending a talk about (yet another) review of the curriculum in Australian schools. The talk and following discussion was conducted according to the Chatham House rule , which I had never encountered before. Previously I wrote about the iron triangle in education: access, cost, and quality. What is the role and significance of curriculum in education? I think it is helpful to make some clear distinctions in roles, responsibilities, and desired outcomes. 1. Students learning. This is what it is all about! It is important to distinguish this from students passing exams, attending lectures, or completing tasks. 2. Effective teachers. They need to be passionate and competent, both about their subject and their students. 3. Curriculum and resources. This also includes textbooks, course handbooks, online resources, buildings, libraries, equipment, laboratories, computers.... 4. Policies and administrative procedures. This includes hiring and fir

What is the "mechanism" and definitive signatures of the Mott metal-insulator transition? If there is an order parameter, what is it? Consider a single band Hubbard model at half-filling. As U/t increases there is a transition from a metal to an insulator. The critical value of U/t is non-zero except for cases (e.g. one dimension or the square lattice) where there is perfect Fermi surface nesting of the metal state. Here is one picture of the transition: the metal to insulator transition is due to binding of holons and doublons. This is advocated by Yokoyama and collaborators and summarised in the Figure below (taken from this paper ). At half filling there are equal numbers of holons and doublons. In the metallic state (left) the holons and doublons are mobile. In the insulating state (right) holons and doublons are bound together on neighbouring sites. Evidence for this picture comes from numerical simulations. Yokoyama, Ogata, and Tanaka consider the followin

A previous post focused on quantum effects largely associated with hydrogen bonding associated with the O-H stretch vibration. Here, I consider effects largely associated with angular motion, known as librational modes. Feynman Path Integral computer simulations performed by Peter Rossky, Bruce Berne, Greg Voth, and Peter Kusalik have led to the following key ideas. 1. Quantum water is less structured than classical water. This is seen in the figure below taken from a 2004  paper by Hernandez de la Pena and Kusalik. 2. This is largely do to quantisation of orientational rather than translational degrees of freedom. The clear evidence for this is from Kusalik's path integral simulations. There, the water molecules are rigid and only the orientational motion of the molecules is quantised. Similar results for the structure factor, (translational) diffusion constant, and orientational relaxation times (and their isotope effects) are obtained from simulations with flexible

When it comes to elemental metals and insulators, a simple signature to distinguish them is the temperature dependence of the electrical resistivity. Metals have a resistivity that increases monotonically with increasing temperature. Insulators (and semiconductors) have a resistivity that decreases monotonically with increasing temperature. Furthermore, for metals the temperature dependence is a power law and for insulators it is activated/exponential/Arrhenius. This distinction reflects the presence or absence of a charge gap, i.e., energy gap in the charge excitation spectrum. Metals are characterised by a non-zero value of the charge compressibility and a non-zero value of the (one-particle) density of states at the chemical potential (Fermi energy for a Fermi liquid). However, in strongly correlated electron materials the temperature dependence of the resistivity is not a definitive signature of a metal versus an insulator. The figure below shows the measured temperatu

Nandan Pakhira and I recent completed a paper Absence of a quantum limit to charge diffusion in bad metals This work was partly motivated by -  a recent proposal , using results from the AdS-CFT correspondence, by Sean Hartnoll that there was a quantum limit to the charge diffusion constant in bad metals, -  experimental observation and theoretical calculations of a limit to the spin diffusion constant in cold atom fermions near the unitarity limit . We calculated the temperature dependence of the charge diffusion constant in the metallic phase of a Hubbard model using Dynamical Mean-Field Theory (DMFT). The figure below shows  the temperature dependence of the charge diffusion constant for a range of values of the Hubbard U. The temperature and energy scale is the half-bandwidth W. The Mott insulator occurs for U larger than about 3.4 W. Violations of Hartnoll's bound occurs in the same incoherent regime as violations of the Mott-Ioffe-Regel limit on the resistivi

At the Journal Club on Condensed Matter, Jason Alicea has a stimulating  commentary on an interesting experimental paper, Two Phase Transitions Induced by a Magnetic Field in Graphite Benoît Fauqué, David LeBoeuf, Baptiste Vignolle, Marc Nardone, Cyril Proust, and Kamran Behnia  In the experiment, the temperature dependence of the resistance of graphite [stacks of layers of graphene] is measured with magnetic fields perpendicular to the layers for fields up to 80 Tesla. [n.b. the high field! This is a pulsed field.] It is estimated that above 7.5 Tesla all the graphene layers are in their lowest Landau level. The figure below shows a colour shaded plot of the interlayer resistance [on a logarithmic scale] as a function of temperature and magnetic field. This is highly suggestive of a phase diagram and that several phase transitions occur as a function of magnetic field. This is highly appealing (seductive?) because there are theoretical predictions [reviewed by Alicea] of

Biman Bagchi has just published a new book, Water in Biological and Chemical Processes: From Structure and Dynamics to Function  Cambridge University Press sent me a complimentary copy to review. I am slowly working through it and will write a detailed review when I am done. I think this is a very challenging subject to write a book on for at least three reasons. First, the scope of the topic is immense. Furthermore, it is multi-disciplinary spanning physics, chemistry, and biology, with a strong interaction between experiment, theory, and simulation. Second, although there have been some significant advances in the last few decades there is real state of flux, with a fair share of controversies, advances, and fashions. Finally, which audience do you write for? Experimental biochemists or theoretical physicists or somewhere in between. Although this is an incredibly important and challenging topic few authors have taken up the challenge. One who has is Arieh Ben-Naim Molecula

Previously I posted about my paper submission strategy. A recent experience highlighted to me the folly of the high stakes game of going down the status chain of descending impact factors: Nature -> Science -> Nature X, PNAS -> PRL, JACS -> PRB, JCP. Two significant problems with this game are: 1. A lot of time and energy is wasted in strategising, rewriting, reformatting, and resubmitting at each stage of the process. Furthermore, if there are multiple senior authors each stage can be particularly slow. 2. Given the low success rates the paper often ends up in PRB or a comparable journal (J. Chem. Phys., J. Phys. Chem.) anyway! I have followed this route and it has been a whole year between submission and publication. In contrast, on 28 July I submitted a paper as a regular article to J. Chem. Phys. and it appeared online on 10 September! Six weeks! I have also had papers published in PRA and PRB much faster than in PRL. Why is speedy publication valuable?

Getting feedback from students via formal evaluations at the end of a course can be helpful, encouraging or discouraging, frustrating, satisfying ... A few weeks ago I got my evaluations for a course I taught last semester. Here are my reflections. First, given there were only 5 they should be taken with a grain of salt! They were very positive which was quite encouraging. They aren't always... I was particularly encouraged that students noticed and appreciated several things I worked on and increasingly emphasise. Giving the big picture and trying to put everything in that context. Having a good textbook [Ashcroft and Mermin, in this case] and following it closely. Making order of magnitude estimates. One student pointed out how my treatment of semiconductors was not as clear at the earlier material. I agree! This was the first time I had taught that part of the course. In contrast, most of the other material I have taught 5-10 times before. Some of it relates closely

Many properties of bulk water, including its many anomalous properties , can be described/understood in terms of the classical dynamics of interacting "molecules" that consist of localised point charges. However, there is more to the story. In particular, it turns out some of the success of classical calculations arise from a fortuitous cancellation of quantum effects. Some quantum effects can just be mimicked by using a higher temperature or a softer potential in a classical simulation. Properties to consider include thermodynamics, structure, and dynamics. Besides bulk homogeneous liquid water, there is ice under pressure, and water in confined spaces, at surfaces, and interacting with ions, solutes, and biomolecules. Distinctly quantum effects that may occur in a system include zero-point motion , tunnelling , reflection at the top of a barrier, coherence, interference, entanglement, quantum statistics, and collective phenomena (e.g. superconductivity). As far as I am

There is a nice paper Tautomerism in Porphycenes: Analysis of Rate-Affecting Factors Piotr Ciąćka, Piotr Fita, Arkadiusz Listkowski, Michał Kijak, Santi Nonell, Daiki Kuzuhara, Hiroko Yamada, Czesław Radzewicz, and Jacek Waluk They look at nineteen different porphycenes, which means that R, the distance between the nitrogen atoms that donate and accept a proton varies. [This is a testimony to the patience and skill of synthetic organic chemists to produce 19 different compounds.] The rate of tautomerization [i.e. double proton transfer] can be measured my monitoring the time dependence of the fluorescence anisotropy because the transition dipole moment of the two tautomers is in different directions, as illustrated below, in the graphical abstract of the paper. The key result is below: the rate of tautomerization [i.e. double proton transfer] versus R. Note the vertical scale varies by three orders of magnitude. For single hydrogen bonds many correlations between R an

I would not claim to be the most organised person. I know I can do better. But, I also know I struggle less than some. Here are a few things that help me to avoid chaos. I don't do all of them all the time, but they are good to aim for. Just say no. The more responsibilities you take on and the busier you get and the harder it is to juggle everything, keep up, think clearly, set priorities, avoid the tyranny of the urgent.... A clear desk I am more relaxed, focused, and productive, if the only thing I have on the desk in front of me is what I am actually working on. Move the piles of other stuff somewhere else, out of view. Google Calendar I have a work calendar and a personal one. I include all my weekly meetings and obligations. Everyone I work with can see the work calendar and knows what I am up to. They can also see "busy" if there is something in the personal one. My family sees both. Keep the schedule Once something is in the calendar it is more or l

There is a nice helpful review Biochemistry and Theory of Proton-Coupled Electron Transfer  Agostino Migliore, Nicholas F. Polizzi, Michael J. Therien, and David N. Beratan Here are a few of the (basic) things I got out of reading it (albeit on a long plane flight a while ago). There are a diverse range of biomolecules where coupled electron-proton transfer plays a key role in their function. The electron transfer (ET) and proton transfer (PT) are usually spatially separated. [See blue and red arrows below]. There are fundamental questions about whether the transfer is concerted or sequential, adiabatic or non-adiabatic, and how important the protein environment (polar solvent)  is. Often short hydrogen bonds are involved and so the nuclear degrees of freedom need to be treated quantum mechanically, in order to take into account tunnelling and/or zero-point motion. Diabatic states are key to understanding and theoretical model development. Although there are some "

I would like to review some important new results on topic X. Several recent studies using some complicated new experimental technique together with large computer simulations have led to new insights and understanding. This is a major advance in the field and attracting significant attention. But there are still many open questions and there remains much work to be done. Did you learn anything from this "review" beyond that X is a hot topic that is generating lots of papers? Unfortunately, I find many "News and Views" or "Perspective" pieces and review articles read a bit like the paragraph above. I would really like to know what specific new insights have been gained and what the open questions are. Why do we often degenerate to the generic? It is actually hard work to figure out what the specific insights are and to clearly communicate them, particularly in a few sentences.

Previously I wrote about the danger of comparing oneself to your peers . It can easily lead to discouragement, anxiety, and a loss of self-confidence. It is also unhelpful for students and postdocs to compare their present advisor/supervisor/mentor  to past advisors. It is also unhelpful for a supervisor to compare their current students/postdocs to previous ones. Early in his career Professor X had an absolutely brilliant student Y who made an important discovery. [Decades later X and Y shared a Nobel Prize for this discovery.] Apparently, X compared all his later students to Y, and could not understand why they could not be as good as Y. Sometimes he even let the students know this. I have also known people who have had an exceptionally helpful undergrad/Ph.D advisor but then were always unhappy with their graduate/postdoc advisor because they just weren't as helpful. Making comparisons is a natural human tendency. Sometimes I struggle with it. But, I try not to. It is o

Science is becoming increasingly inter-disciplinary. Most science graduates do not end up working in scientific research or an area related to their undergraduate major. Yet most undergraduate curricula are essentially the same as they were fifty years ago and are copies of courses at MIT-Berkeley-Oxford designed for people who would go on to a Ph.D and (hopefully) end up working in research universities. Biology and medicine are changing rapidly particularly in becoming more quantitative. How should we adapt to these realities? Are there any existing courses that might be appropriate for every science major to take? Sometimes my colleagues get upset that advanced physics undergrads don't know certain things they should [Lorentz transformations, Brownian motion, scattering theory, ....]. But, my biggest concern is that they don't have certain basic skills [dimensional analysis, sketching graphs, recognising silly answers,  writing clearly, ....]. These skills will be imp