Condensed concepts

It is rather amazing that many complex systems, ranging from proteins to stock markets to cities, exhibit power laws, sometimes over many decades. A critical review is here , which contains the figure below. Complexity theory makes much of these power laws. But, sometimes I wonder what the power laws really tell us, and particularly whether for social and economic issues they are good for anything. Recently, I learnt of a fascinating case. Admittedly, it does not rely on the exact mathematical details (e.g. the value of the power law exponent!). The case is described in an article by Dudley Herschbach , Understanding the outstanding: Zipf's law and positive deviance and in the book Aid at the Edge of Chaos , by Ben Ramalingam. Here is the basic idea. Suppose that you have a system of many weakly interacting (random) components. Based on the central limit theorem one would expect that a particular random variable would obey a normal (Gaussian) distribution. This means

Almost three years ago I posted  about the controversy concerning whether the photoactive yellow protein has low-barrier hydrogen bonds [for these the energy barrier for proton transfer is comparable to the zero-point energy]. I highlighted just how difficult it is going to be, both experimentally and theoretically to definitively resolve the issue, just as for an enzyme I recently discussed. A key issue concerns how to interpret large proton NMR chemical shifts. Two recent papers weigh in on the issue The Low Barrier Hydrogen Bond in the Photoactive Yellow Protein: A Vacuum Artifact Absent in the Crystal and Solution  Timo Graen, Ludger Inhester, Maike Clemens, Helmut Grubmüller, and Gerrit Groenhof A Dynamic Equilibrium of Three Hydrogen-Bond Conformers Explains the NMR Spectrum of the Active Site of Photoactive Yellow Protein  Phillip Johannes Taenzler, Keyarash Sadeghian, and Christian Ochsenfeld I think the caveats I have offered before need to kept in mind. As with un

Are you looking for Christmas gifts? I think that scientists should be writing popular books for the general public. However, I am disappointed by most I look at. Too many seem to be characterised by hype, self-promotion, over-simplification, or promoting a particular narrow philosophical agenda. The books lack balance and nuance. We should not be just explaining about scientific knowledge but also give an accurate picture of what science is, and what it can and can't do. (Aside: Some of the problems of the genre, particularly its almost quasi-religious agenda, is discussed in a paper by my UQ history colleague, Ian Hesketh.) There is one book I that I do often hear non-scientists enthusiastically talk about. A Short History of Nearly Everything by the famous travel (!) writer Bill Bryson. There is a nice illustrated edition. I welcome comments from people who have read the book or given it to non-scientists.

Today I am giving a talk in the Applied Physics Department at Stanford. My host is Sri Raghu . Here is the current version of the slides.

Carbonic anhydrase is a common enzyme that performs many different physiological functions including maintaining acid-base equilibria. It is one of the fastest enzymes known and its rate is actually limited not by the chemical reaction at the active site but by diffusion of the reactants and products to the active site. Understanding the details of its mechanism presents several challenges, both experimentally and theoretically. A key issue is the number and exact location of the water molecules near the active site. The most recent picture (from a 2010 x-ray crystallography study ) is shown below. The "water wire" is involved in the proton transfer from the zinc cation to the Histidine residue. Of particular note is the short hydrogen bond (2.4 Angstroms) between the OH- group and a neighbouring water molecule. Such a water network near an active site is similar to what occurs in the green fluorescent protein and KSI. Reliable knowledge of the finer details of t

My wife and I are often looking for new science demonstrations to do with children. The latest one she found was "bouncing soap bubbles". For reasons of convenience [laziness?] we actually bought the kit from Steve Spangler. It is pretty cool. A couple of interesting scientific questions are: Why do the gloves help? The claim is that the grease on your hands makes bursting the bubbles easier. Why does glycerin make the soap bubbles stronger? Why does "ageing" the soap solution for 24 hours lead to stronger bubbles? Journal of Chemical Education is often a source of good ideas and science discussions. Here are two relevant articles. Clean Chemistry: Entertaining and Educational Activities with Soap Bubbles  Kathryn R. Williams Soap Films and the Joy of Bubbles Mary E. Saecker

Previously, I posted about a historical precedent for managing by metrics: economic planning in Stalinist Russia. I recently learnt of a capitalist analogue, starting with Ford motor company in the USA. I found the following account illuminating and loved the (tragic) quotes from Colin Powell  about the Vietnam war. Robert McNamara was the brightest of a group of ten military analysts who worked together in Air Force Statistical Control during World War II and who were hired en masse by Henry Ford II in 1946. They became a strategic planning unit within Ford, initially dubbed the Quiz Kids because of their seemingly endless questions and youth, but eventually renamed the Whiz Kids , thanks in no small part to the efforts of McNamara.   There were ‘four McNamara steps to changing the thinking of any organisation’: state an objective, work out how to get there, apply costings, and systematically monitor progress against the plan . In the 1960s, appointed by J.F. Kennedy as Secre

The challenge of understanding phase transitions and proton ordering in hydrogen-bonded ferroelectrics (such as KDP, squaric acid, croconic acid ) and different crystal phases of ice has been a rich source of lattice models for statistical physics. Models include ice-type model s (six-vertex model, Slater's KDP model), transverse field Ising model, and some gauge theories. Some of the classical (quantum) models are exactly soluble in two (one) dimensions. An important question that seems to be skimmed over is the following: under what assumptions can one actually "derive" these models starting from the actual crystal structure and electronic and vibrational properties of a specific material? That quantum effects, particularly tunnelling of protons, are important in some of the materials is indicated by the large shifts (of the order of 100 percent) seen in the transition temperatures upon H/D isotope substitution. In 1963 de Gennes argued that the transverse fi

On Friday I am giving a talk in the Chemistry Department at Berkeley. Here is the current version of the slides. There is some interesting local background history I will briefly mention in the talk. One of the first people to document correlations between different properties (e.g. bond lengths and vibrational frequencies) of diverse classes of H-bond complexes was George Pimentel.  Many correlations were summarised in a classic book, "The Hydrogen Bond" published in 1960. He also promoted the idea of a 4-electron, 3 orbital bond which has similarities to the diabatic state picture I am promoting. There is even a lecture theatre on campus named after him!

Here is a helpful quote from William Bialek. It is a footnote in a nice article,  Perspectives on theory at the interface of physics and biology . The Boltzmann distribution is the maximum entropy distribution consistent with knowing the mean energy, and this sometimes leads to confusion about maximum entropy methods as being equivalent to some sort of equilibrium assumption (which would be obviously wrong). But we can build maximum entropy models that hold many different expectation values fixed, and it is only when we fix the expectation value of the Hamiltonian that we are describing thermal equilibrium. What is useful is that maximum entropy models are equivalent to the Boltzmann distribution for some hypothetical system, and often this is a source of both intuition and calculational tools. This type of approach features in the statistical mechanics of income distributions. Examples where Bialek has applied this includes voting patterns of the USA Supreme Court , flocking of b

Beginning in 2007 luxury journals published some experimental papers making claims that quantum coherence was essential to photosynthesis. This was followed by a lot of theoretical papers claiming support. I was skeptical about these claims and in the first few years of this blog wrote several posts highlighting problems with the experiments, theory, interpretation, and hype. Here is a recent paper that repeats one of the first experiments. Nature does not rely on long-lived electronic quantum coherence for photosynthetic energy transfer Hong-Guang Duan, Valentyn I. Prokhorenko, Richard Cogdell, Khuram Ashraf, Amy L. Stevens, Michael Thorwart, R. J. Dwayne Miller During the first steps of photosynthesis, the energy of impinging solar photons is transformed into electronic excitation energy of the light-harvesting biomolecular complexes. The subsequent energy transfer to the reaction center is understood in terms of exciton quasiparticles which move on a grid of biomolecular sit

The common narrative in physics is that the limitations of reductionism, the importance of emergence, and the stratification of scientific fields and concepts were first highlighted in 1972,  by P.W. Anderson in a classic article, "More is Different" published in Science . Anderson nicely used broken symmetry as an example of an organising principle that occurs at one strata and as a result of the thermodynamic limit. The article was based on lectures Anderson gave in 1967. The article actually does not seem to contain the word "emergence". He talks about new properties "arising". I recently learned how similar ideas about emergence and the stratification of fields was enunciated earlier by Michael Polanyi , in  The Tacit Dimension , published in 1966, based on his 1962 Terry Lectures at Yale. The book contains a chapter entitled "Emergence". Here is a quote: you cannot derive a vocabulary from phonetics; you cannot derive the grammar o

The New York Times has an interesting Op-ed. piece  Quit Social Media. Your Career May Depend on It , by Cal Newport , a faculty member in computer science at Georgetown University. When I saw the headline I thought the point was going to be an important one that has been made many times before; people sometimes post stupid stuff on social media and get fired as a result. Don't do it! However, that is not his point. Rather, he says social media is bad for two reasons: 1. It is a distraction that prevents deep thinking and sustained  "deep" work. Because you are constantly looking at your phone, tablet, or laptop or posting on it, you don't have the long periods of "quiet" time that are needed for substantial achievement. 2. Real substantial contributions will get noticed and recognised without you constantly "tweeting" or posting about what you are doing or have done. Cut back on the self-promotion. Overall, I agree. When I discussed th

The spin-1 antiferromagnetic Heisenberg chain provides a nice example of emergence in a quantum many-body system. Specifically, there are three distinct phenomena that emerge that were difficult to anticipate: the energy gap conjectured by Haldane, topological order, and the edge excitations with spin-1/2. An interesting question is whether anyone could have ever predicted these from just knowing the atomic and crystal structure of a specific material. I suspect Laughlin and Pines would say no. To understand the emergent properties one needs to derive effective Hamiltonians at several different length and energy scales. I have tried to capture this in the diagram below. In the vertical direction, the length scales get longer and the energy scales get smaller. It is interesting that one can get the Haldane gap from the non-linear sigma model. However, it coarse grains too much and won't give the topological order or the edge excitations. It seems to me that the profund

It has dubious origins. Some people are very impressed that I have a Wikipedia page. I find this a bit embarrassing because there are many scientists, more distinguished than I, who do not have pages. When people tell me how impressed they are I tell them the story. Almost ten years ago some enthusiasts of "quantum biology" invited me to contribute a chapter to a book on the subject. The chapter I wrote, together with two students, was different from most of the other chapters because we focussed on realistic models and estimates for quantum decoherence in biomolecules. (Some of the material is here. ) This leads one to be very skeptical about the whole notion that quantum coherence can play a significant role in biomolecular function, let alone biological processes. Most other authors are true believers. I believe that to promote the book one of the editors had one of his Ph.D. students [who appeared to also do a some of the grunt work of the book editing] create a

One of the key predictions of the  diabatic state picture of hydrogen bonding  is that there should be an excited electronic state ( a twin state ) which is the "anti-bonding" combination of the two diabatic states associated with the ground state H-bond. Recently, I posted about  a possible identification of this state in malonaldehyde. The following recent paper is relevant. Symmetry breaking in the axial symmetrical configurations of enolic propanedial, propanedithial, and propanediselenal: pseudo Jahn–Teller effect versus the resonance-assisted hydrogen bond theory Elahe Jalali, Davood Nori-Shargh The key figure is below. The lowest B2 state is the twin state. In the diabatic state picture, Delta is half of the off-diagonal matrix element that couples the two diabatic states. Similar diagrams occur when O is replaced with S or Se. The paper does not discuss twin states, but interprets everything in terms of the framework of the   ( A 1  +  B 2 ) ⊗  b 2  p

Sometimes when I speak about science to church groups I show the old (1977) video Powers of Ten which nicely illustrates the immense scale of the universe and orders of magnitude. I often wished there was a more polished modern version. Yesterday it was pointed out to me there is,  Cosmic Eye . The phone app can be purchased here  for $1.

In 2011 it was proposed that pyrochlore iridates (such as Y2Ir2O7) could exhibit the properties of a Weyl semi-metal, the three-dimensional analog of the Dirac cone found in graphene. Since the sociology of condensed matter research is driven by exotica this paper stimulated numerous theoretical and experimental studies. However, as often is the case, things turn out to be more complicated and it seems unlikely that these materials  exhibit a Weyl semi-metal. This past week I have read several nice papers that address the issue. Variation of optical conductivity spectra in the course of bandwidth-controlled metal-insulator transitions in pyrochlore iridates K. Ueda, J. Fujioka, and Y. Tokura There is a very nice phase diagram which shows systematic trends as a function of the ionic radius of the rare earth element R=Y, Dy, Gd, ... Most of the materials are antiferromagnetic insulators. The colour shading describes the low energy spectral weight in the optical conductivi

I am very disturbed at how I encounter people, particularly young people, who work ridiculously long hours. Furthermore, it worries me that some are deluded about what they might achieve by doing this. Due to a variety of cultural pressures I think Ph.D. students from the Majority World are particularly prone to this. First let's not debate exactly how many hours is too many or exceptions to the generalisations below. At the end I will give some caveats. Here are some reasons why very long hours are not a good idea. Something may snap. And, when it does it will be very costly. It may be your mental or physical health, or your spouse, or your children, ... Don't think it won't happen. It does. Long hours may be making you quite inefficient and unproductive. You become tired and can't think as clearly and so make more mistakes, have less ideas, and find it harder to prioritise. It is a myth that long hours is mostly what you need to do to survive or prosper

Through a nice blog post by Anshul Kogar, I became aware of a beautiful Physics Today Reference Frame (just 2 pages!) from 1998 by Frank Wilczek Why are there Analogies between Condensed Matter and Particle Theory? It is worth reading in full and slowly. But here a few of the profound ideas that I found new and stimulating. A central result of Newton's Principia was "to prove the theorem that the gravitational force exerted by a spherically symmetric body is the same as that due to an ideal point of equal total mass at the body's center. This theorem provides quite a rigorous and precise example of how macroscopic bodies can be replaced by microscopic ones , without altering the consequent behavior. "  More generally, we find that nowhere in the equations of classical mechanics [or electromagnetism] is there any quantity that fixes a definite scale of distance . Only with quantum mechanics do fundamental length scales appear: the Planck length, Compton

It is strange that I have never done this. Furthermore, I don't know anyone who does. Why do this? First, it is helpful for me to think about and decide what my goals actually are, particular relating to the big picture. Second, it will be helpful for students to know. Too often they are guessing. Even worst, I fear that most just assume that my goals are theirs. Then they get frustrated if/when they discover their goals and/or values  are different. So here are some goals I could think of. They are listed in order of decreasing importance to me. To help you learn to THINK. To inspire you to learn. To help you see this is a beautiful subject. To help you learn skills that are useful in other endeavors (including outside physics). The help you put this subject in the context of others. To help you learn the technical details of the subject. To be your ally not your adversary  . My goals are NOT the following. (Listed in no particular order). To make you happy

Time has a direction. Macroscopic processes are irreversible. Mixing is a simple example. The second law of thermodynamics encodes universal property of nature. Yet the microscopic laws of nature [Newton's equations or Schrodinger's equation] are time reversal invariant. There is no arrow of time in these equations. So, where does macroscopic irreversibility come from? It is helpful to think of irreversibility [broken time-reversal symmetry] as an emergent property. It only exists in the thermodynamic limit. Strictly speaking for a finite number of particles there is a " recurrence time " [whereby the system can return to close to its initial state]. However, for even as few as a thousand particles this becomes much longer than any experimental time scale. There is a nice analogy to spontaneously broken symmetry in phase transitions.  Strictly speaking for a finite number of particles there is no broken symmetry as the system can tunnel backwards and forwards

I welcome comments on this preprint. Quantum critical local spin dynamics near the Mott metal-insulator transition in infinite dimensions Nagamalleswararao Dasari, N. S. Vidhyadhiraja, Mark Jarrell, and Ross H. McKenzie Finding microscopic models for metallic states that exhibit quantum critical properties such as $\omega/T$ scaling is a major theoretical challenge. We calculate the local dynamical spin susceptibility $\chi(T,\omega)$ for a Hubbard model at half filling using Dynamical Mean-Field Theory, which is exact in infinite dimensions. Qualitatively distinct behavior is found in the different regions of the phase diagram: Mott insulator, Fermi liquid metal, bad metal, and a quantum critical region above the finite temperature critical point. The signature of the latter is $\omega/T$ scaling where $T$ is the temperature. Our results are consistent with previous results showing scaling of the dc electrical conductivity and are relevant to experiments on organic charge transfe

Today I am giving the first talk in a session on Computational materials science at the  4th International Conference on Advances in Materials and Materials Processing . Here are the slides for my talk "The role of simple models and concepts in computational materials science". I will be referring the audience to the article such as those mentioned here , here and here t hat give a critical assessment of computer simulations and stress the importance of concepts. I welcome comments, particularly as I think the talk could be stronger and clearer.

Like everything in India, higher education is incredibly diverse, both in quality, resources, and culture. These statistics give some of the flavour. There are about 800 universities. A significant distinction is between state and central universities. The former are funded and controlled by state governments. The latter (and IITs, IISERs, IISc, TIFR...)  are funded and controlled by the central (i.e. national/federal) government. Broadly, the quality, resources, and autonomy (i.e. freedom from political interference) of the latter is much greater. On my many trips to India I have only visited these centrally funded institutes and universities. This afternoon I looking forward to visiting the Physics Department of Vidyasagar University . It is funded by the West Bengal state government, and was started in 1981. It is named in honour of Ishwar Chandra Vidyasagar, a significant social reformer from the 19th century. I am giving my talk on "Emergent Quantum Matter". Here a

Today I am giving a seminar, "Effect of quantum nuclear motion on hydrogen bonding" in the Chemistry Department at IIT Kharagpur . My host is Srabani Taraphder . Here are the slides . The talk is mostly based on this paper.

Today I am giving a seminar in the Physics Department at Indian Institute of Technology (IIT) Kharagpur , "Frustrated organic Mott insulators: from quantum spin liquids to superconductors." Slides are  here . Due to the recent Nobel Prize to Haldane, I included one slide about quantum spin liquids in one dimension. The talk material is covered in great detail in a  review article , written together with Ben Powell .

For a diverse range of chemical compounds, the strength of hydrogen bonds [parametrised by the binding energy and/or bond length] is correlated with a wide range of physical properties such as bond lengths, vibrational frequencies and intensities, and isotope effects. I have posted about many of these and a summary of the main ones is in this paper. One correlation which is particularly important for practical reasons is the correlation of bond strength (and length) with the chemical shift associated with proton NMR. The chemical shift is the difference between the NMR resonant frequency of the proton in a specific molecule and that of a free proton. The first important point is that although this shift is extremely small (typically one part in 100,000!) one can measure it extremely accurately. More importantly, this shift is quite sensitive to the local chemical bonding and so one can use it to actually identify the bonding in unknown molecules (e.g. protein structure determin

Today I am giving a talk at IISER Kolkata. My host Chiranjib Mitra requested that I include some discussion of this year's Nobel Prize in Physics. This was very helpful as I think the talk now flows better and there are more illustrations of my main points. But, there is less time to talk about my own work... Here is the current version of the slides . I welcome comments.

I like concrete classroom demonstrations. Andrew Boothroyd recently showed me a very elegant demonstration based on this paper Spontaneous Chirality in Simple Systems Galen T. Pickett, Mark Gross, and Hiroko Okuyama It considers hard spheres confined to a cylinder. Different phases depending on the value of D, the ratio of the diameters of the cylinder and the spheres. The phase diagram is below. Andrew has a nice demonstration using ping pong balls and a special transparent plastic cylinder that has the right diameter to produce a chiral phase. He shows it during a colloquium and sometimes even gets an applause! I found a .ppt that has the nice pictures below.

Amongst his one page guides John Wilkins [my postdoc supervisor] has Guidelines for giving a truly terrible talk "Strict adherence to the following time-􏰀tested guidelines will ensure that both you and your work remain obscure and will guarantee an audience of minimum size at your next talk􏰁." Independently, David Sholl has illustrated the problems in concrete ways with an actual talk "The Secrets of Memorably Bad Presentations"   I am not sure if it is funny or just plain painful. But it does drive home the points. All students (and some faculty) should be forced to watch it in full.

A necessary ingredient to surviving and possibly prospering in science is the ability to write clearly in English. Yet many students are not native English speakers and some have had poor education and training. For some, it is even difficult to write basic sentences without grammar and spelling mistakes. This is a serious issue for both students and advisors. Unfortunately, what happens too often is that advisors spend too much time correcting the English in drafts of papers and thesis chapters rather than focusing on the scientific content . Even, worse lazy or over-committed advisors don't do the corrections and referees, examiners, or editors are left with the problem. Advisors, co-authors, and examiners can get quite irritated in the process. Students need to realise they are really hurting themselves in not addressing this issue. Is there a solution? I try to encourage students and postdocs to pair up and read each other's drafts. However, this is not really qui

In my previous post about the 2016 Nobel Prize in Physics I stated that the Kosterlitz-Thouless transition was a classical phase transition (involving topological objects = vortices), in contrast to the quantum phase transitions associated with topological phases of matter. However, on reflection I realised that it should not be overlooked that there is something distinctly quantum about the KT transition. In a two-dimensional superfluid it involves the binding of pairs of vortices and anti-vortices. These each have a quantum of circulation (+/-h/m where h is Planck's constant and m is the particle mass). At the KT transition temperature Tc there is a finite jump in the superfluid density rho. The value just below Tc is related to Tc by Note that Planck's constant appears in this equation. In a classical world (h=0), Tc would be zero and there would be no KT transition! This universal relation was derived by Nelson and Kosterlitz in 1977 The figure below c

Are there any necessary or sufficient conditions for getting a faculty position? Previously, I suggested that a key element is actually dumb luck: being in the right place at the right time. But that is not my focus here. Twenty years ago when I was struggling to find a faculty job the mythology was that you had to have at least two PRLs and get an invited talk at an APS March Meeting. And doing a postdoc at certain places (e.g. ITP Santa Barbara) would help... Now the mythology seems to be that you need to have Nature and Science papers.... But, this in actually not the case. This is not a sufficient condition. Search committees want to hire someone who can lead an independent research program and can move into new areas. Several department chairs have said things to me along the lines of "It is amazing how we interview some candidates who have impressive publication lists involving papers in luxury journals but when we actually talk to them we quickly lose interest.

I was delighted to see this year's Nobel Prize in Physics awarded to Thouless, Haldane, and Kosterlitz  ”for theoretical discoveries of topological phase transitions and topological phases of matter”. A few years ago I predicted Thouless and Haldane , but was not sure they would ever get it. I am particularly glad they were not bypassed, but rather pushed forward, by topological insulators. There is a very nice review of the scientific history on the Nobel site. Here are a few random observations, roughly in order of decreasing importance. First, it is important to appreciate that there are two distinct scientific discoveries here. They do both involve Thouless and topology, but they really are distinct and so Thouless’ contribution in both is all the more impressive. The “topological phase transition” concerns the Kosterlitz-Thouless transition which is a classical phase transition (i.e. driven by thermal fluctuations) which is driven by vortices (topological objects,