Condensed concepts

In my recent tutorial on bad metals at IISER Pune a student asked me a basic question that I could not answer: "Why is the degenerate Fermi gas called "degenerate"? Is it anything to do with degenerate energy levels?" So, I went in search for answers. The Wikipedia entry on Degenerate matter is a bit rambling and I found it unhelpful. I then went to the library and looked at a few textbooks and found a range of answers. Some books use the term "degenerate" without any elaboration. In the discussion below it seems looking at the Oxford dictionary is helpful: Having lost the physical, mental, or moral qualities considered normal and desirable; showing evidence of decline.   technical: Lacking some usual or expected property or quality , in particular. Here are a few entries degenerate. (This use of the word is completely unrelated to its other use to describe a set of quantum states that have the same energy). Daniel V. Schroeder, An Int

There are several things that I used to find very puzzling about electrical noise measurements on the metallic phase of organic charge transfer salts. The  measured noise spectrum is close to (but not exactly) 1/f. The disparity of time/energy scales. What is the relationship (if any) between the noise (which is sometimes measured on time scales as long as one thousand seconds (mHz)) and microscopics (which one might calculate with quantum chemistry and/or Hubbard models, but typically involves energies larger than meV or frequencies that can be ten orders of magnitude larger)? Obscure trends. If one looks at the actual exponent alpha of the noise, 1/f^alpha. It varies in a non-monotonic way as the temperature T varies. This looks rather "random" to me (i.e. I found it hard to believe there was any systematics involved). However, Jens Muller and collaborators have used a model due to Dutta, Dimon, and Horn  (DDH) to nicely elucidate what is going on in a serie

After yesterday's colloquium a large group of IISER students (both undergraduate and graduate) expressed an interest in having a tutorial on more of the subject of emergent quantum matter. It is today at 6pm after they are done with the days lectures. This tells you something about the quality of the students and institution! I am going to give a tutorial about bad metals. I will probably cover half of these slides . Hopefully there will be lots of questions and side discussions on the blackboard.

On monday I am giving a talk at the Indian Institute for Science Education and Research (IISER ) Pune. Here is the current version of the slides.

One helpful way to think about condensed matter is in terms of relative energy scales. This can help one decide what is important and what is not. However, this does not always work, particularly in complex systems where new low energy scales can emerge. For a long time there has been a "minor detail" about organic charge transfer salts based on the BEDT-TTF molecule that I have found rather annoying and puzzling. It concerns the role of ethylene end groups on the molecule and their possible different conformations (eclipsed vs. staggered). Why should the conformations matter? I would think not. The overlap of the relevant electronic molecular orbitals which are largely centred on sulphur atoms are negligible as seen below in the HOMO (Highest Occupied Molecular Orbital) for a BEDT-TTF dimer. The figures are taken from this  paper by Edan Scriven and Ben Powell. However, things are more subtle than I would have thought. Here are some of the significant ef

" SciPost is a a complete scientific publication portal managed by active professional scientists. " It is worth checking out. SciPost addresses many concerns I have about the current sorry state of science and publishing. These include that  journals becoming redundant and counter productive  and so we need alternative publication models , particularly not involving for-profit companies. One thing I particularly like is the transparency. All the referee reports are public and referees have the option of being anonymous or not. Furthermore, anyone can write a report. Authors responses to the reports are also public. I think this public accountability may raise standards significantly. I hope you (and I) will consider supporting it by -  submitting articles - writing referee reports (either on request or volunteering) - writing commentaries - being willing to serve on the Editorial College Jean-Sebastien Caux is to be commended for all the work he has put into

When I learnt and later taught basic quantum mechanics I don't think the notion of energy level repulsion (or equivalently avoided crossings) was emphasised (or even discussed?). Much later I encountered the idea in advanced topics in theoretical physics such as random matrix theory and in theoretical chemistry  (non-adiabatic transitions and conical intersections). Yet level repulsion is a very simple phenomena that can be illustrated with just a two by two matrix describing two coupled quantum states, as nicely discussed on the Wikipedia page . Last semester when I was teaching Solid State Physics I realised just how central and basic the phenomena is and that the students did not appreciate this. Level repulsion is the origin of several key phenomena in chemistry and physics. In solid state physics, it is the origin of the appearance of band gaps at the zone boundary and thus the all important distinction between metals and insulators. Previously, I posted how

Previously, I have posted about how in certain contexts one can relate non-equilibrium transport quantities to equilibrium thermodynamic quantities. This is particularly nice because for theorists it is usually a lot easier to calculate the latter than the former. But, it should be stressed that all of these results are an approximation or only hold in certain limits. Here are some examples. The thermoelectric power can be related to the temperature derivative of the chemical potential through the Kelvin formula (illuminated by Peterson and Shastry) . A paper argues that the Weidemann-Franz ratio in a non-Fermi liquid can be related to the ratio of two different susceptibilities. Work of Shastry showing that the high frequency limit of the Hall coefficient, Lorenz ratio and thermopower can be related to equilibrium correlation functions. It has been suggested that the transverse thermoelectric conductivity (Nernst signal) due to superconducting fluctuations is closely relat

That is the point! Mentally healthy people are rational and reasonable (within the bounds of human fallibility!). They are not driven or paralysed by amplified anxieties, phobias, mood swings, suicidal thoughts, depression, "black clouds", ... Yet, often people struggle to understand and/or be empathetic with someone suffering from mental illness because they are not thinking and/or acting in a "rational" manner. This dismissal or diminishing of what is going on can even be done by a sufferer themself, "I know I am having all these crazy thoughts and feelings, but I know they are crazy so it does not matter.... I don't need to get help." or... The person is so far gone that they actually think that their irrational thoughts are rational. It is everyone else who is crazy... Here two good recent articles about mental health by physicists. The plight of the postdocs: Academia and mental health There’s an awful cost to getting a PhD that no

There is nothing new in this post. But the issue  keeps coming up. I have written many posts about this before. My last one was Advice to undergrads giving research talks. Perhaps the following basic point gets lost in all the suggestions. Keep it simple. In almost every situation, most of your audience knows very little about your specific research topic. In some cases, they know virtually nothing about your actual research field. Thus, you need to cut out almost all the technical details and give plenty of background and motivation. But again, you need to realistic. Don't kid yourself that in 5 minutes you are going to teach them Density Functional Theory or Two-dimensional NMR spectroscopy. Have modest goals. Teach the audience some interesting science. Convince them that your topic/field is interesting and important. Show them you have achieved something concrete and interesting. Don't bore people. But perhaps, these are ambitious goals because most talks

I find it surprising that is almost three years since I my last post on this topic.  I guess I try not to be too negative too often... Vox has a very long article, The 7 biggest problems facing science, according to 270 scientists . It is worth reading and I largely agree with it. Possible concrete solutions are discussed. Many of the issues I have discussed on this blog and so it is both encouraging and discouraging to see others voice the same concerns. I think a significant positive change would occur if the luxury journals (especially the pernicious Nature Publishing Group) were banned/boycotted and put out of business. Funding agencies could simply say you can't use our money to do research that you publish in them. And in future applications you can't list any such publications from before 2017 on your CV. I know it is not going to happen. But we do need to at least acknowledge that if it did that a lot of problems would be diminished.

My son brought to my attention an Econtalk podcast   that has an interesting discussion of emergence. Here is some of the transcript. I've become so fascinated by the prairie as a metaphor for emergent order . And some things have to emerge and grow in an organic way. And I've referenced this book--it's by Shona Brown and Kathleen Eisenhardt; it's called Competing on the Edge . It's actually a management book. It's not about emergent order per se, and it's not about wildlife or prairies literally.  [Here is a long but beautiful quote from the book]. Imagine yourself at O'Hare at a far different time, not in 1998 but in 1898, or even in 1798, before the patchwork quilt of roads, fences, and farms had changed the Midwestern landscape forever. Around you would be an abundance of plants, long grasses of various colors, a pallette of flowers, some trees. You'd see the original "amber waves of grain." If waited a little while, you'd also

It is hard to believe that we really don't understand the basic issues that I am going to discuss. Resitivity occurs in a metal because scattering causes decay of charge currents. This means that the total momentum of the electrons in the presence of an electric field decays. However, in a Fermi liquid metal with strong electron-electron interactions the main scattering of electrons is due to electron-electron scattering. But, in such collisions the total momentum of the two electrons is the same before and after the collision. One can calculate the life time of the quasi-particles and it is inversely proportional to the temperature squared. The quasi-particle scattering rate ~ T^2. Suppose one makes the relaxation time approximation in the Boltzmann equation or equivalently, neglects vertex corrections in the corresponding current-current correlation function associated with the Kubo formula for the conductivity. Then the resistivity is proportional to the quasi-particle sc

Today I am giving a  seminar  at the  Institute of Physics in Belgrade . My host is  Darko Tanaskovic  who has done  nice work using DMFT to study bad metals and quantum criticality. Here is the current version of the  slides. The main results are in  this paper.