Condensed concepts

Just write it! Stop procrastinating. Take responsibility. Don't wait for permission, guidance, or feedback from your supervisor, advisor, committee, or anyone else. The more you have written and "complete" the greater the pressure on the supervisor, department, and university, to o.k. submission of the thesis. With supervisors who are tardy/slack/lazy/negligent/disorganised about feedback make sure meetings, submissions of drafts, and requests for feedback are documented in emails.

I have been looking at some books about better writing since next year I am going to be giving a couple of workshops on this.  I was really intrigued that one book mentioned the Flesch Reading Ease Score which is defined by the equation: A sign that this is a "widely accepted" metric is that it is incorporated in Microsoft Word. The main thing that bothers me is the number of significant figures in the coefficients. But also, surely you could devise the metric so that it actually does give values in the range 0-100, like most guides claim. Pathological text can produces negative values or values greater than 100.

This xkcd cartoon features in an interesting article in the Economist Triumph of the nerds about how the internet has changed the world of cartoons.

What determines the excited state lifetime of a chromophore in a solvent? What are the relative importance of the polarity of the solvent [dielectric relaxation time] and the viscosity? The key physics associated with the solvent polarity is that the dipole moment in the ground and excited states are usually different and so the solvent relaxes and there is an associated redshift of the emission. The viscosity is particularly relevant when there is intramolecular twisting and this motion is usually overdamped. This problem is of fundamental interest because it concerns  overdamped quantum dynamics. It is of applied interest because significant biomolecular sensors make use of the sensitivity of specific chromophores [e.g. Thioflavin-T binding to amyloid fybrils]. Two recent papers from Dan Huppert's group raise three important questions for me. An Accounts in Chemical Research Molecular Rotors: What Lies Behind the High Sensitivity of the Thioflavin-T Fluorescent Marker?

Yesterday I did some science demos at a kids holiday club, using the Coke-Mentos fountain . Previous efforts led to the post  Developing science demonstrations that actually teach science . It is fun and cool to do spectacular demonstrations that cause kids to go "Wow!" and think that science is "fun". But these also need to be a vehicle to teach something about critical thinking and the process of doing science. Small initiatives can help. For example, I had one child record the height of each of the fountain, that was estimated by the group. This emphasized that measurement, error estimation, record keeping, and comparisons are key parts of doing science. Aside: Yesterday I thought the Coke-Mentos fountain was higher than last time, particularly for diet Coke. I suspect the fact that is was a hot day helped, increasing the solubility of the carbon dioxide? We also did Film canister rockets  which the kids always enjoy. I found it amusing that the kids ran o

For the excited state dynamics of a specific chromophore in a solvent what are the essential degrees of freedom (electronic, vibrational, and solvent) that must be included in a model Hamiltonian? What determines if the excited state dynamics is classical, semi-classical, or fully quantum? Under what conditions does the Born-Oppenheimer approximation break down? For a specific photochemical reaction what are the relevant vibrational degrees of freedom? What determines the relative importance of stretching, torsional, and pyramidal vibrations? What determines the branching ratio for passage through a conical intersection? Relevant parameters may be the slope at the intersection, slanting, size of the wavepacket, and the distance of closest approach (impact parameter) What is the interplay of the electronic, vibrational and solvent degrees of freedom in excited state dynamics? What determines the relative importance of the viscosity and the polarity

What is the physical code that relates the amino acid sequence to a proteins native structure? How do proteins fold so fast? Can protein structure be computationally predicted? These are highlighted as key questions in a nice readable review in Science  The Protein Folding problem, 50 years on  by Ken Dill and Justin MacCallum. The article gives a sober assessment of limited but significant achievements and the substantial challenges ahead.

Tony Wright brought to my attention a nice (brief) review paper on the arXiv Magnetotransport and induced superconductivity in Bi based three-dimensional topological insulators M. Veldhorst, M. Snelder, M. Hoek, C. G. Molenaar, D. P. Leusink, A. A. Golubov, H. Hilgenkamp, A. Brinkman [published version is here ]. In passing, I note there is a brief section on Shubnikov de Haas oscillations and the Berry phase. A more extensive discussion can be found in a recent preprint by Tony Wright and I. Here I briefly discuss the very nice section about linear magnetoresistance (LMR)  (i.e. a magnetoresistance that increases linearly with magnetic field, in contrast to the quadratic increase characteristic of regular metals) that have been observed in Bi-based topological insulators. This was of particular interest to me because I previously posted about the puzzle of linear magnetoresistance in Ag2Te [which may or may not be a topological insulator]. Similar issues and theoretical mode

Following  my post Impact factors have no impact on me , a question was raised about the role of impact factors in different disciplines and whether they are useful for making comparisons. Factoring impact  describes a history Ph.D student's perspective on first encountering impact factors.

Distinguishing cause and correlation in complex systems is always a tricky matter. There is an interesting preprint Ion-size effects in cuprate superconductors - implications for pairing B.P.P. Mallett, T. Wolf, E. Gilioli, F. Licci, G.V.M. Williams, A.B. Kaiser, N. Suresh, N.W. Ashcroft, J.L. Tallon For a large family of cuprates they observe correlations between the basal plane area of the unit cell, the Heisenberg antiferromagnetic exchange J , the maximum superconducting Tc, and the total electric polarizability of the ions. The main result from this rather impressive systematic study is in the Figure below The upper graph shows that Tc (max) decreases with increasing J, contrary to what one might expect from spin fluctuation mediated (or RVB) type pictures of superconducitivity (see e.g. this paper which found the pairing amplitude scaled roughly with J). The lower graph shows that Tc (max) increases with increasing ionic polarizability. The authors then make the

Bei-Lok Hu has a nice paper on the arXiv, Emergence: Key physical issues for deeper philosophical inquiries . The acknowledgements end with the poignant (and sad) observation:   This kind of non mission-driven, non utilitarian work addressing purely intellectual issues is not expected to be supported by any U.S. grant agency.

To the experienced this post may seem a bit basic but I think it does concern something really important that students must learn and researchers should not forget. It is a very simple idea but when continually applied it can be quite fruitful. Understanding and teaching condensed matter became a lot easier when I began to appreciate this. In considering any phenomena in condensed matter it is important to have good estimates (at least within an order of magnitude) of the different energy scales associated with different interactions and effects. I give several concrete examples to illustrate. To understand why Fermi liquid theory works so well for elemental metals (sodium, magnesium, tin, ...) the first step is estimating the Fermi energy, the thermal energy (k_B T), the Zeeman energy in a typical laboratory field, ... A step towards the BCS theory of superconductivity was appreciation of the profound disparity of energy scales, condensation energy much less than k_B T_c comp

There is a useful post For the ambitious prospective Ph.D student: a guide . It is written by Rachael Meager, an undergraduate at Melbourne University, about how Australian students can get into top 10 Economics Ph.D programs, largely in the USA. Much of the advice is also relevant to science and engineering programs, and I suspect beyond Australia. It is also relevant to Australian students who want to get a high first class honours result so they can get a Ph.D scholarship within Australia, in a leading research group. I thought it was cute she recommended writing comments on faculty blogs to make them aware of your existence, interest, and sophistication. Lots of economics faculty write blogs. In the Australian context I would also suggest that students consider limiting or quitting part-time jobs (McDonald's etc.) unless it is a matter of not eating. The average Australian undergraduate works something like 10-20 hours per week. It is simply not possible to do this and

Doug Natelson has a nice post Things no one teaches you as part of your training  which discusses some of the crucial skills that scientists (whether university faculty or industrial managers) must have but are never taught. These include managing people, writing, being a good colleague, ... The assumption is that these skills are hopefully absorbed by osmosis. One could argue that they should be more explicitly taught, even if only informally. One that is particularly important to experimentalists and I had not thought about is managing budgets. Consumables, and equipment purchase and maintenance can easily blow out. If there isn't enough money for these then a lab can grind to a halt. Some of the comments list useful resources for helping learn some of these skills.

Although I have written several papers about it I still struggle to understand the Berry phase and how it is or may be manifested in solids. Recent reading, summarised below, has helped. There is a nice short review  Geometry and the anomalous Hall effect in ferromagnets N. P. Ong and Wei-Li Lee As late as 1999 Sundaram and Niu wrote down the semi-classical equations of motion for Bloch states in the presence of a Berry curvature, script F below. (1) and (2) below. n.b. how there is a certain symmetry between x and k. The last equation gives the "magnetic monopoles" associated with the Berry connection/. Aside: the Berry connection Omega_c is the analogue of the magnetic field. It is related to the curvature F tilde by (F tilde)_ab= epsilon_abc Omega_c. The Berry connection is related to the Berry phase in the same sense that a magnetic field is associated with an Aharonov-Bohm phase. The above text is taken from a beautiful paper  Berry Curvature on the Fermi

There is a nice article on the arXiv,  Simulations: the dark side by Daan Frenkel Here is an extract to give you the flavour Although this point of view is not universally accepted, scientists are human . Being human, they like to impress their peers. One way to impress your peers is to establish a record. It is for this reason that, year after year, there have been – and will be – claims of the demonstration of ever larger prime numbers: at present – 2012 – the record-holding prime contains more than ten million digits but less than one hundred million digits. As the number of primes is infinite, that search will never end and any record is therefore likely to be overthrown in a relatively short time. No eternal fame there. In simulations, we see a similar effort: the simulation of the ‘largest’ system yet , or the simulation for the longest time yet (it is necessarily ‘either-or’). Again, these records are short-lived. They may be useful to advertise the power of a new computer,

The (Sommerfeld-)Wilson ratio is an important quantity to characterise strongly correlated Fermi liquids. Chapter 5 of Hewson's book The Kondo Problem to Heavy Fermions describes the Fermi liquid theory of the Anderson single impurity model. One can derive the identity which relates the impurity spin susceptibility, charge susceptibility, and the specific heat coefficient gamma. In the Kondo regime the charge susceptibility is zero and this leads to the fact that the Wilson ratio has the universal value of exactly two. It is interesting that one can derive the same identity for the exact (Bethe ansatz) solution to the Hubbard model in one dimension. See equation (7) in this  paper  by Tatsuya Usuki, Norio Kawakami, and Ayao Okiji. As a result one finds the Wilson ratio is always less than 2. As the band filling tends towards one-half the Mott insulator is approached, the charge susceptibility diverges and the Wilson ratio W tends to zero. See the Figure below.

The dynamics of the atomic motion associated with most chemical reactions is classical. In particular, the rate of reaction is determined by the rate of thermal excitation over an energy barrier associated with the transition state (a key concept): a particular nuclear configuration which is a saddle point on the potential energy surface which contains both the reactants and products. It is hard to find exceptions to this paradigm, e.g., where quantum tunneling below the barrier is important. Some people claim this picture breaks down for enzymes, as discussed in an earlier post . But I remain to be convinced, particularly that enzymes have evolved to make use of quantum tunneling. However, I am convinced and fascinated by an article which does discuss some concrete exceptions to transition state theory for small molecules that have recently been discovered. Tunneling does not just lead to quantitative changes in reaction rates but different products of the chemical reaction. Th

Previously, I considered the tricky problem of Does the doped Hubbard model superconductor? I mentioned in passing a worrying quantum Monte Carlo study published in PRB in 1999 Correlated wave functions and the absence of long-range order in numeri cal studies of the Hubbard model M. Guerrero, G. Ortiz, and J. E. Gubernatis The graph below shows the distance dependence of the pairing correlation function in the d-wave channel. If superconductivity occurs it should lend to a non-zero value equal to the square of the superconducting order parameter. It certainly looks like it tends to zero at large distances. However, careful examination shows that it seems to have a non-zero value of order 0.001. Perhaps, that is just a finite size effect. But, we should ask, " How big do we expect the long-range correlations, i.e. the magnitude of the square of the order parameter d, to be? " A cluster DMFT calculation on the doped Hubbard model (in the PRB below) gives a value

There seems to be a common view that on CVs (and grant applications) people should list the Impact Factors for each journal in which they have a paper. To me this "information" is just noise and clutter. I do not include it in my own CV or grant applications. Why? 1. IFs just encode something I know already. Nature > Science > PRL ~ JACS > Phys. Rev B ~ J. Chem. Phys. > Physica B ~ Int. J. Mod. Phys. B > Proceedings of the Royal Society of Queensland ..... 2. There is a large random element in success or failure to get an individual paper published in a high profile journal. e.g., who the referees are. 3. The average citations of a journal is not a good measure of the significance of a specific paper. There is a large variance. What really matters is how much YOUR/MY specific paper in that journal is cited in the long term. Unfortunately, in most cases it is hard to know in less than 3-5 years. 4. Crap papers can get published in Nature and Science.

Last week we struggled through chapter 4, "Renormalisation group calculations" of Hewson's book, The Kondo Problem to heavy fermions. The focus is on Kenneth Wilson's numerical treatment of the Kondo problem, mentioned in his Nobel prize citation. Much of it still remains a mystery to me... Here are a few key aspects. Please correct me where I am wrong or at least confused... First, he mapped the three-dimensional Kondo model Hamiltonian into a one dimensional tight binding chain (half-line) with single impurity spin at the boundary. This simplification makes the problem more numerically tractable. Next, he used a logarithmic discretization (in energy) of the states in the conduction band. This important step is motivated by the logarithmic divergences found by Kondo's perturbative calculation and Anderson's poor man's scaling arguments. He then numerically diagonalises the Hamiltonian with a discrete set of states for a finite chain. One then re

Weston Borden's article 40 years of fruitful chemical collaborations  has an significant observation concerning writing effective papers: focus on the physical explanation of the results rather than on the details of the methodology. He recounts how he he learnt this, while starting out as an Assistant Professor at Harvard, in a collaboration with Lionel Salem . Borden had performed some calculations using the Pariser-Parr-Pople (PPP) model for the electronic structure of conjugated organic molecules [for physicists an extended Hubbard model with long-range Coulomb interactions]. Lionel read my draft, and he promptly rewrote it. Lionel’s revised version, which was the one that we published , focused much more than my draft had on the explanation of the PPP results, rather than on the details of the calculations. This experience taught me a valuable lesson. Although describing the details of calculations and the results obtained from them is certainly important, it is even more

Many previous posts have considered how in a metallic phase close to a Mott insulator one can observe a crossover from a Fermi liquid to a bad metal with increasing temperature. One observes something quite different in FeSi (iron silicide) which has been a subject of debate for several decades. Different paper titles include the following words: Kondo insulator, ferromagnetic semiconductor, unconventional charge gap, strong electron-phonon coupling, Anderson-Mott localization, singlet semiconductor, covalent insulator, correlated band insulator, ferromagnetic metal, .... At low temperatures FeSi is a semiconductor with a gap of about 50 meV (500 K). Both the spin susceptibility and the resistivity are gapped. However,  around 200 K there is a crossover to a bad metal. The spin susceptibility has a maximum versus temperature around 400 K and above that can be fitted to a Curie-Weiss form, suggesting the presence of local moments. The thermopower has a maximum around 50 K with a c

There is a very nice article in the Journal of Organic Chemistry With a Little Help from My Friends: Forty Years of Fruitful Chemical Collaborations by Weston Thatcher Borden Borden's career is unusual in that he has done both organic synthesis [i.e., actually making molecules] and computational quantum chemistry. The article is worth reading for several reasons. It describes some -interesting organic chemistry and shows how quantum chemistry has illuminated it -characteristics of fruitful collaborations, both between theorists and between theorists and experimentalists -interesting history and personal vignettes and perspectives On the latter I found the following throwaway line rather disturbing and disappointing: When I was an Assistant Professor at Harvard, unlike most of my colleagues in the Chemistry Department, Bill Doering   seemed genuinely interested in talking about chemistry with me. Unfortunately, this happens too often. I would be curious to know why

Topological insulators (TIs) are certainly a hot topic. However, there are two things that might make one nervous about all the excitement. 1. All the materials being studied as TIs [e.g. Bi2Se3] actually aren't TIs. What!? A TI is by definition a bulk insulator  with surface metallic states that are topologically protected. However, the actual materials turn out not to be bulk insulators. On a practical level this makes separating out bulk and surface contributions, particularly in transport measurements, tricky. But, also presents an ideological problem: one is not actually studying the phase of matter one wishes one was studying. 2. One could argue that TIs are "just a band structure effect", i.e., they do not involve any quantum many-body physics. However, these objections are put to rest by a preprint Discovery of the First True Three-Dimensional Topological Insulator: Samarium Hexaboride Steven Wolgast, Cagliyan Kurdak, Kai Sun, J. W. Allen, Dae-Jeong Kim,

There is a paper in Science this week  Flows of Research Manuscripts Among Scientific Journals Reveal Hidden Submission Patterns The authors claim,  Resubmissions were significantly more cited than first-intents published the same year in the same journal....  ... these results should help authors endure the frustration associated with long resubmission processes and encourage them to take the challenge  Then I looked at the data below to see how strong the claimed effect was. I think the horizontal lines mark the mean and the box shows the variance. Hence, it looks to me like citations may increase by less than 10% with resubmission. This hardly seems on any significance to me. But, am I missing something? Maybe this is another issue of comparisons are in the eye of the beholder  or the silly claims that journals make about their impact factors or some faculty make about their student evaluations.

Chapter 3 of Hewson's The Kondo Problem to Heavy fermions reviews Anderson's poor man's scaling treatment of the Kondo model. Starting with the anisotropic Kondo Hamiltonian one rescales the electronic bandwidth D and see how the interactions J_z and J_ and J+ rescale. To lowest order in perturbation theory this leads to the renormalisation group equations Solving these gives the flow diagram below A few important consequences 1. Antiferromagnetic (AFM) interactions flow to strong coupling. 2. The Kondo energy/temperature is invariant to the flow. 3. This is an example of asymptotic freedom  [interactions can weaker at higher energies]. It is impressive that Anderson did this before Wilson and Fisher used renormalisation group ideas to describe critical phenomena in classical phase transitions. It is fascinating that the same flow equations and flows describe the Kosterlitz-Thouless phase transition  associated with topological order [vortex p

I can fully imagine a grant reviewer, tenure or hiring committee saying that when reviewing the "impact" of a particular publication of an individual. Furthermore, one can also say "the paper was in PRL but it was a full 12 months between submission and publication. Clearly, he was lucky to get in PRL at all..." But, there is a problem with all this. These observations apply to Duncan Haldane's 1988 paper  Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" Haldane's paper has been receiving about 100 citations per year for the past few years. It now has a total of 530 citations in Physical Review journals. However, from 1988 to 1999 it received only 17 citations. Hardly impressive.

Last week we read "Beyond perturbation theory", chapter 3 of Hewson's The Kondo Problem to Heavy Fermions. First he gives, without derivation, perturbation expressions for the impurity spin susceptibility and specific heat. The results exhibit logarithmic divergences at temperatures of the order of the Kondo temperature. Hewson discusses some of the herculean efforts in the 1960s of people such as Abrikosov, Suhl, and Hamann, to come up with new diagrammatic techniques and summations to get rid of, or at least reduce, the divergences. The results still have logarithmic temperature dependences. None give the Fermi liquid like dependences at low temperatures that experiments hinted at. The Kondo effect is non-perturbative . n.b. the Kondo temperature has a non-analytic dependence on J. What does one do? An important insight was variational wave function proposed by Yosida in 1966. One finds that the ground state is a spin singlet between the impurity spin and a

Seth Olsen  and I are about to advertise for a postdoc to work with us at UQ. The flavour of our interests and approach can be seen in posts on this blog under labels such as  organic photonics ,  quantum chemistry , conical intersections, and Born-Oppenheimer approximation. A draft of the official position description is here . We anticipate an official advertisement will appear shortly. Please contact us if you are interested.

Some of my colleagues, may say "Yes!". However, this post is mostly concerned with moving from academia to industry and is mostly directed at graduate students and postdocs. However, some of the issues are also relevant to faculty considering a change of institution. The issues are based on my limited experience and observations over almost three decades. I stress that I am not saying that all the realities below are right or just, only that they are realities that may need to be faced. Its personal. Different people have different values. How much do you value (or don't value) independence, freedom, money, family time, flexible work hours, job "security", affirmation, geographic location, ....? The relative value you place on such things will significantly affect what job may be suitable for you and whether and when you decide to make a change? A job that is great for your friend may be horrible for you and visa versa. There is no simple right answer.

This post follows up on earlier posts including Connecting the pseudogap to superconductivity in the organics There is a nice paper Pseudogap and Fermi arc in κ-type organic superconductors by Jing Kang, Shun-Li Yu, Tao Xiang, and Jian-Xin Li They use Cluster Perturbation Theory to study the Hubbard model on the anisotropic triangular lattice at half filling. They calculate the one-electron spectral function using clusters as large as 12 sites [embedded self-consistently in an infinite lattice]. The authors find three distinct phases: Mott insulator, Fermi liquid, and a pseudogap state with Fermi arcs. The latter occurs in between the two other phases. The Figure below shows an intensity map of the spectral function at the Fermi energy for U=4t and t'=0.7t. This clearly shows a complete Fermi surface (with hot spots). As U increases towards the Mott phase, U=5t one sees parts of the Fermi surface gap out leaving Fermi arcs. Note the cold spots [red region=low scatteri