Condensed concepts

In a 2007 Nature paper Engel et al. reported the data below showing the amplitude of an optical signal versus time. The lower curve is the Fourier transform [using a new numerical method they developed explicitly for this paper] of the upper data. They interpreted this data as evidence for quantum coherence between the excited states of different chromophores in a photosynthetic protein, since an oscillatory signal is a signature of quantum interference (Rabi oscillations). Engel et al. went on to claim that this coherence enabled the biomolecule to function in a highly efficient manner because: …the system is essentially performing a single quantum computation, sensing many states simultaneously and selecting the correct answer, as indicated by the efficiency of the energy transfer. In the presence of quantum coherence transfer, such an operation is analogous to Grover's algorithm , …such a scheme can provide efficiency beyond that of a classical search algorithm. This Natur

Almost anyone can cobble together some powerpoint slides. But, actually preparing a good talk is very hard work. This is on my mind because this week I am working on a colloquium I am giving this friday. Why is it hard work, even for the experienced? Because you have to decide what material to leave out!

Over the past decade there has been an amazing set of experiments performed which involve seeing quantum interference associated with the wave nature of very large molecules. The figure below is taken from a nice review article by Markus Arndt and Klaus Hornberger. It shows some of molecules, including as many as one hundred atoms and of the order of one thousands of elementary particles (protons, neutrons, and electrons). The figure below shows some of the interference fringes seen. Occasionally I hear these incredible experiments used as a "proof of principle" to justify the possible role of significant quantum effects in biology. However, I think this a fanciful view because of the following significant constraints in the experiments: They involve single molecules They are performed in vacuum. The quantum interference is associated with the centre of mass degree of freedom. By, definition this does not couple to all the internal degrees of freedom. This is a very long

This week the UQ Physics Colloquium was given by John Cook on  Communicating Climate Science and Countering Disinformation.  He is a UQ physics graduate and now writes an influential blog  Skeptical Science which aims to present peer-reviewed climate science in an accessible fashion that answers climate change skeptics. He has also developed a popular Phone application which answers 10 common used arguments of climate change skeptics. He recently published a book Climate Change Denial . Here is my summary of some of the main points. 97 out 100 climate scientists believe that humans are causing carbon dioxide levels to rise. Why?  There are many different lines of evidence. In contrast, only 58% of the general public believe this. This is because the mainstream media gives the impression of a 50/50 debate. Several references were made to a book Merchants of Doubt "  by Naomi Oreskes and Erik Conway which documents how vested financial interests have funded disinformation c

As little as possible! What? Occasionally when I review grant proposals I am dismayed by the large amount of money that some people, especially junior people, ask for. I wonder who, if anyone, is advising them to do this. A few things to consider when you prepare your proposed budget: The greater the requested budget the greater the scrutiny of the application. If your budget is 2 or 3 times the budget of competing applications the funding agency will almost always think that it is better to fund 2 or 3 groups rather than just one. Getting some money is always better than getting none, especially if you are starting out. The kudos of actually getting the grant is fairly weakly dependent of how much money you actually get. The maximum possible allowed budget is not a good guide as to how much you should ask for. A better guide is the average size of grants previously given to applicants of comparable stature and experience to you. And if you do get the grant, but the budget is tr

I recently gave two lectures on superconductivity to a fourth year undergraduate Condensed Matter Physics course. In hindsight, there are few points that I did not discuss but should have included: the relevance of BCS theory and Cooper pairing to nuclear physics and neutron stars how the Meissner effect can be viewed as a photon obtaining mass and that this idea is key to electro-weak theory and to the Higgs boson These issues are nicely discussed in an article  Superconductivity's Smorgasbord of Insights: A Movable Feast by Adrian Cho which appeared in Science last month to celebrate the Centenary of Kamerlingh Onnes discovery. It contains the figure below.

I am trying to understand under exactly what conditions it is (or is not) meaningful to use a self energy to describe and understand experiments on a strongly correlated metal which may be (at least in some sense) a non-Fermi liquid. This is particularly motivated by a recent paper on the overdoped cuprates. Below are some statements which I am trying to ascertain the truth of and relationship between them. I believe 1. and 2. are always true. 3. and 4. are equivalent but are not always true. 5. is true. I am not sure about 6. 1. The one-electron Greens function G(k,E) is an analytic function of energy E. 2. One can always define a self energy by Dyson's equation where G0 is the non-interacting Greens function. This self energy will be an analytical function of E. 3. If E is treated as a complex variable G(k,E) has isolated simple poles in the complex plane. These poles correspond to quasiparticles. One can then write down a Boltzmann transport equation for these q

Broken symmetry is one of the most important concepts in physics from the second half of the twentieth century. Hence, surely all undergraduate physics majors should learn it. Here are the slides from a lecture I gave last week to PHYS2020 Thermodynamics and Condensed Matter. In the lecture and (in a tutorial) I get the students to try and solve the problem below.   I then illustrate the solution (and the associated equal angles) with bee hives and some videos of soap films. This version is taken from the book  Introduction to statistical physics  by Herson Huang.  I first encountered the problem in my second year of graduate school when Jim Sauls (later to become my advisor) in the very first lecture of a graduate condensed matter course asked students to solve it "cold" [right there in the lecture and hand in a solution] without the suggested form of the solution given above.  I would be interested if someone knows the associated history of this problem.

Compared to some fields (e.g. biology, high energy physics, philosophy, history, movies, historical theology) I think most Wikipedia articles on condensed matter physics and theoretical chemistry are sporadic in quality. It would be wonderful if someone took the initiative and time to improve them. I keep trying to encourage students to do this but not succeeding. But, that is another story.... The actual purpose of this post is just to highlight some of the actual content of a really nice entry on the Magnetic flux quantum , [h/2e] which states: The magnetic flux quantum may be measured with great precision by exploiting the  Josephson effect . In fact, when coupled with the measurement of the  von Klitzing constant  R K  = h/e 2 , this provides the most precise values of  Planck's constant  h obtained to date. This is remarkable since h is generally associated with the behavior of microscopically small systems , whereas the quantization of magnetic flux in a superconductor and

This is not easy. It is worth the effort. You want to convince people to attend your talk: it will be interesting, important and understandable. Things to do: tailor your abstract to your audience (e.g. their backgrounds and interests) explain why the topic is interesting use words sparingly find a balance between being generic and too technical include some key scientific ideas you will discuss include a brief statement of your main results include a few relevant references the really keen may want to look at re-write it several times (especially if you are in-experienced) Things to avoid superfluous phrases such as "In this talk I will..." and "I will end with some conclusions". using acronyms: nLAs, DFT, LDA+DMFT, NMR, ENDOR etc.  hype But, it is always easier to tell people what to do rather than actually do it yourself! So I offer up for critique my latest abstract: for the UQ Physics Colloquium next friday. Quantifying the limited role of quan

Last week I gave half a lecture  on the phase diagram of helium and superfluidity to a second year undergraduate class on Thermodynamics and Condensed Matter Physics . The lecture includes: a discussion of the differences between the phase diagrams of 3He and 4He a list of the 4 Nobel Prizes awarded for work in superfluidity [Landau, Kapitsa, Osheroff, Richardson, and Lee, Leggett] (I did not include BECs but should have] a video of the superfluid transition a discussion of an amazing experiment on the space shuttle which determined the critical exponent for the specific heat at the superfluid (lambda) transition to five significant figures.

I particularly like the Figure below taken from a paper  The radical character of the acenes: A density matrix renormalization group study  by Johannes Hachmann, Jonathan Dorando, Michael Avilés, and Garnet Chan. HUNO = highest occupied natural orbital           LUNO = lowest occupied natural orbital Note how as the acene gets longer the spread in orbital occupation number increases. In a nice review article Schmidt and Gordon state: The presence of occupation numbers between 0.1 and 1.9 indicates considerable multireference character.  (Multi-reference character means how many Slater determinants are required to describe the state.) It seems to me that the spread in the above distribution gives a measure of the number orbitals M one needs to include in the active space of a Complete Active Space (CAS) calculation. In a Hartree-Fock calculation the occupations are all 2 or 0. The number of natural orbital occupations that deviate significantly from 2 or 0 is a good measure of M

I just received by snail mail the December 2010 issue of  Physics Today.  The  whole issue  is devoted to  Subrahmanyan Chandrasekhar , marking the centenary of his birth. There is a fascinating and challenging article Some memories of Chandra by Robert Wald  and four other scientists, including Roger Penrose. Wald states: Of all the scientists I have met, Chandra had the highest standards for both intellectual rigor and personal integrity. He applied those standards most uncompromisingly to himself , but he also did not tolerate failings by others in such matters. He was particularly intolerant of scientists motivated primarily by the hope of receiving recognition from others rather than by a deep, inner conviction that their work was of importance and interest, whatever anyone else might think. He was equally intolerant of scientists who rested on their laurels or were otherwise lazy or sloppy, rather than applying their full intellectual efforts toward their work.

This week I have been re-reading Phil Anderson's paper,   The `strange metal' is  a Fermi liquid with edge singularities . Here is a brief summary of some of the main things I gleaned from the paper. The question is: What is the nature of the excitations (and one-electron Greens function) of the Hubbard model in the infinite-U limit and for large dopings (perhaps x greater than 0.3) above which superconductivity occurs? Anderson claims: the strong interactions lead to a significant particle-hole asymmetry [which should be visible in tunneling spectra]  excitations exhibit anomalous forward scattering the quasi-particle weight Z vanishes on the Fermi surface there is  a formal similarity of this problem with that of Fermi-edge singularities in the X-ray spectra of metals, where the one-electron Greens function has a power law decay associated with the phase shift from an infinite potential. A simple argument (exploiting the Friedel sum rule) gives the main quantitative pr

In honour of the 100th anniversary of the discovery of superconductivity Julien Bobroff and collaborators developed a really cool  site  meant for the general public. It contains many videos and discussions of basic science. Two particular videos are of interest, one a general introduction to the subject and the other historical details about the original discovery. I also really liked the video below.

A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown , within the framework of applicability of its basic concepts. Albert Einstein Thermodynamics is a great source of both profound and humorous quotes. Many are collected at Wikiquote  and on a site due to Franco Nori. Some morbid but fascinating discussion about the mental health and suicides of many famous pioneers of thermodynamics and statistical mechanics are on a somewhat strange site Encyclopedia of Human Thermodynamics .

Last week I gave a single lecture on Fermi liquids to the honours year undergraduate course PHYS4030 Condensed Matter Physics. The slides do not include the expression for the quasi-particle lifetime or the rough argument  (based on phase space considerations) used to justify its form. This is because I do that on the whiteboard. Perhaps such an important topic justifies more than one lecture...

My wife brought to my attention a New York Times article Improving the Science of Teaching Science  which discusses a recent Science paper  Improved Learning in a Large-Enrollment Physics Class .  Science Now has this summary : Any physics professor who thinks that lecturing to first-year students is the best way to teach them about electromagnetic waves can stop reading this item. For everybody else, however, listen up: A new study shows that students learn much better through an active, iterative process that involves working through their misconceptions with fellow students and getting immediate feedback from the instructor. The research, appearing online today in Science, was conducted by a team at the University of British Columbia (UBC), Vancouver, in Canada, led by physics Nobelist Carl Wieman. First at the University of Colorado, Boulder, and now at an eponymous science education initiative at UBC, Wieman has devoted the past decade to improving undergraduate science instru

For a while I have been uneasy about the use of "etc." in papers, talk slides, grant applications, etc. I see too many sentences like "this research has important implications for chemistry, physics, materials science, etc." or "quantum theory can describe atoms, molecules, etc." Somehow, it communicates to me laziness on the part of the author. Intuitively, I think I object when it is not completely clear or universally agreed upon what the "etc." actually is. I found it helpful to read the Wikipedia page for Et cetera which states The phrase et cetera is often used to delete the logical continuation of some sort of series of descriptions. For example, in the following expression... We will need a lot of bread: wheat, granary, wholemeal, etc. ... the "etc." stands for "and other types of bread". So, if you have actually not thought out what you would list instead of "etc." or if others may disagree with y

A key question concerning the metallic state of cuprate superconductors is: to what extent they can be described by s omething like a Fermi liquid with quasi-particle excitations? As the doping increases away from the Mott insulating state this is more likely to be possible. If it is possible one should be able to define an electronic self energy for the metallic state. Many experiments have been interpreted in these terms. But there are fundamental questions, particularly stressed by Phil Anderson (and embodied in his Hidden Fermi liquid theory ) about whether this is really possible, even in the overdoped region. Jure Kokalj and I have just finished a paper  Consistent description of the metallic phase of overdoped cuprate superconductors as an anisotropic marginal Fermi liquid We consider a model electronic self energy , motivated by Angle-Dependent Magneto-Resistance (ADMR) experiments, and consisting of two terms: The first term has the frequency and temperature dependence o

When my kids were younger and we were on sabbatical in the UK we came across the wonderful series of kids books, Horrible History and Horrible Science.  Below is a scan of the pages on the laws of thermodynamics. Note the stereo-typically British view of Australians (bunch of lazy boozers)! If you click on the images you can see a larger view.

Previously I have posted that one key to giving a good talk is to never offer undefendable ground . i.e., don't make dubious claims that will distract your audience from your main point and undermine your credibility. On Friday at UQ,  David Jamieson , Head of the School of Physics at the University of Melbourne gave a colloquium  Physics, Power, and Climate change. I found the colloquium rather disappointing and frustrating because he made a number of debatable claims. But, perhaps I mis-heard or mis-understood him. I welcome others to clarify or correct me. 1. He began by briefly promoting his own research saying " it is difficult to imagine future technologies if you are not working in our centre ", referring to the ARC Centre for Quantum Computing and Communication Technologies , which works on the Quantum Internet. 2. Chemists may find  strange the claim that quantum computing was essential to understanding how caffeine works. 3. People in the majority wor

Today I read a beautiful paper, Coherence-Incoherence and Crossover and the Mass-Renormalization Puzzles in Sr2RuO4 by Jernej Mravlje, Markus Aichhorn, Takashi Miyake, Kristjan Haule, Gabriel Kotliar, and Antoine Georges The paper is another victory for Dynamical Mean-Field Theory (DMFT) as it shows how LDA+DMFT calculations can give a quantitative description of a whole range of experiments on this strontium ruthenate. Aside and context: This material originally attracted a lot of interest because it is a transition metal oxide with the same perovskite crystal structure as the cuprate superconductors. But, it turns out to be very different because it has a Fermi liquid metallic state and the superconductivity is triplet rather than singlet. But here are some physical insights I found particularly interesting in the paper a. It explains why the coherence temperature and band renormalisation (effective mass) is different for the different bands, and not just determined by the

I must be getting old. Often as people get older they start to trace their family genealogy to learn "where they came from". I had been told since I was a child that my paternal great-great-grandfather was   Samuel Shannon , one of the first Jewish settlers in Australia. But, I had heard that scientists sometimes like to trace their academic lineage, where their Ph.D advisor is their parent, and the advisor of their advisor is their grandparent, and so on. Indeed there is a Mathematics Genealogy project which traces everyone back to Euler and Gauss... So I got intrigued and checked out my own lineage. I was oblivious to this, beyond who my "great-grandfather" was. But, I did not know he had such a distinguished lineage. Finding the rest of my lineage was quite easy using Wikipedia because it listed the advisors of most of my "forebears". Here is the line: Helmholtz Arthur Webster (Founder of the American Physical Society) Albert Wills Isidor Rab

I find coming up with new tutorial, assignment, and exam questions.  Choosing which questions to use is a challenge. Here are some questions I have used over the years in a fourth year undergraduate Condensed Matter Physics course based on Ashcroft and Mermin. I welcome comments on these questions and links to resources for other questions. One useful resource [which I should look at more often] is Solid State Physics: Problems and Solutions by Mihaly and Martin.

I was surprised when the speaker at todays Physics colloquium [which was on climate change] David Jamieson kept referring to Svante Arrhenius as a physicist. I always thought he was chemist! This claiming of Arrhenius as "one of our own" probably irritated me a little because the speaker made some other claims which I felt were rather debatable [perhaps more on that in another post...]. So I went and read the Wikipedia page on Arrhenius which turns out to be pretty fascinating reading [e.g. the almost failed thesis which got him the Nobel Prize! and the commitment to eugenics...]. I now concede you could argue that he was a physicist, because he seems to have done a degree in physics and mostly worked in physics institutes. However, he basically worked on and helped found what today is called physical chemistry (electrolytes and reaction kinetics). His contribution to understanding the greenhouse effect was certainly from the perspective of a physical chemist. He was awa

Today I gave a lecture on First-order phase transitions including a derivation of the Clausius-Clapeyron relation . Students particularly like watching the video of the barrel crush . I also use the video as the basis for a tutorial and sometimes exam questions. It is a nice way to illustrate how big the slope of the liquid-vapour phase boundary is. They also enjoy the ice bomb video.

Angle-Dependent Magneto-Resistance (ADMR) is a powerful technique to map out the Fermi surface properties of a quasi-two-dimensional metal [see this earlier post]. I have worked on the theory of ADMR for more than a decade now and it continues to provide new challenges and applications to new classes of materials [see for example this talk ]. I was delighted to see recently a PRL by an Aussie Rules football team [18 co-authors!] from Japan which has used ADMR to map out some of the Fermi surfaces for one of the new Iron Pnictide superconductors, KFe2As2 [these are in the Class II which exhibit some evidence for superconducting gap nodes]. The figure below shows the angular dependence of the interlayer magnetoresistance at different magnetic field strengths. This is the resulting two Fermi surfaces within the most conducting layers. The authors note that the cross-sectional areas of the Fermi surfaces found by a range of techniques: ADMR (12 and 17% of the FBZ), one ARPES study

I believe physicists and chemists can learn a lot from each other, particularly when it comes to strong electron correlations. However, getting them to spend time together requires a powerful match-maker, particularly given all the communication problems... I have earlier written many separate posts about quantum chemistry and about dynamical mean-field theory (DMFT). The latter has led to significant progress in our understanding of strongly correlated electron materials including the Mott transition in the Hubbard model, and bad metals. Two papers have just appeared which look at possible marriages between DMFT and quantum chemistry, a PRL from Columbia and a J. Chem. Phys. from Cornell. I am reading them but look forward to comments from others.