Probing non-equilibrium dynamics in a quantum many-body system

This week at UQ there was a fascinating Quantum Science Seminar by Jorg Schmiedmayer, describing some beautiful ultra cold atom experiments.  Much of the talk is nicely discussed in a book chapter Does an isolated quantum system relax? [Answer is yes].
Some of the most recent results are in a Science paper, Experimental observation of a generalised Gibbs ensemble that appeared this month.

The experiments involve a one-dimensional Bose gas that can be described as a Luttinger liquid. This means that many properties, even non-equilibrium ones, can be calculated analytically and compared to experiment. This is a theorists dream!

Here are a few things that stood out.

Relaxation from a non-equilibrium state to the thermal equilibrium state occurs on several different time scales. First there is rapid relaxation to a "quasi-steady state" described by a Generalised Gibbs ensemble [This idea goes back to Jaynes] that involves an effective temperature [that one can even theoretically calculate in terms of the bose gas interaction strength].

There is a characteristic length scale associated with the relaxation.

One can even directly measure higher order correlation functions (4th, 6th and 10th order!), as seen below. Furthermore, in a Luttinger liquid [a non-interacting boson field theory] these should factorise in terms of the 2nd order correlation function [reflecting Wick's theorem]. One can even test this experimentally.

One can also simulate the sine Gordon theory and vary the coupling constant and so move through the associated phase transition.

Sabbaticals are undervalued

Take one if you can.

A great privilege and opportunity of having a tenured faculty position is the possibility at most institutions of taking a sabbatical. Roughly one year away for every six years of service or one semester away every seventh semester.

I am concerned that increasingly many faculty don't take sabbaticals and that some institutions or departments (at least in Australia) discourage them. I think they are particularly important for Australians because of our geographic isolation. [For some strange reason at UQ it is called a Special Studies Program].

There are many obstacles to taking sabbaticals: finance, family commitments, keeping a group running, inertia, .... For some US faculty they also have to come up with some of the salary....

I have actually only ever taken one sabbatical (Oxford in 2004). However, for the past 12 years I have had few teaching and admin. responsibilities and have had freedom to travel. I am actually in the process of applying for one for the second half of 2016. As part of the process I had to recycle the report I wrote at the end of the last one about my activities and how I and the university benefited. I recalled that it was a productive time that lead to new ideas and collaborations. But, only reading the report did I recall just how great the benefits were. Much of what happened in the following five years or so would not have been possible without things that happened on the sabbatical.

So take one! Encourage your colleagues to as well! I think they are especially important for people weighed down with heavy teaching and/or admin responsibilities.

Are sabbaticals becoming less common? Why? Have you benefitted from one or more?

Don't confuse necessary and sufficient conditions

In Carl Caves recent UQ Quantum Science Seminar "Quantum metrology meets Quantum Information Science" as an aside he also made an important side point.

People often erroneously assume that the converse of a statement is true (i.e.  A implies B means that B implies A). This came up because a few referees had said that some of the results he presented in the seminar were "obvious". Roughly speaking, this concerns the issue of trying to determine what input quantum state to an interferometer will produce a "physical" output state. He found that the input state had to be "physical" (by some well-defined technical criteria). Showing this is non-trivial. However, it is obvious a physical input state is sufficient to produce a physical output state. But, that does not mean it is necessary. Showing this turned out to be quite non-trivial.

I can immediately think of two other cases where scientists made similar errors of conflating necessary and sufficient conditions.

The first case is the existence of quasi-crystals. It was well known that a periodic array of atoms is sufficient to produce sharp diffraction peaks. However, many people erroneously assumed that this was also necessary. I emphasise this point when I teach undergraduates about quasi-crystals.

The second concerns Angle-dependent MagnetoResistance Oscillations in quasi-two-dimensional metals. Not long after their experimental discovery AMRO was explained in terms of a coherent interlayer transport and a three-dimensional Fermi surface. It was subsequently more or less assumed that observing AMRO was evidence for a three-dimensional Fermi surface.  However, in 1998, Perez Moses and I showed that a 3D Fermi surface was not necessary for the existence of AMRO.

Is quantum entanglement really needed?

On tuesday at UQ Carl Caves gave a Quantum Science Seminar "Quantum metrology meets Quantum Information Science".

One side point he made was that just because quantum entanglement is glamorous and beloved by luxury journals does not mean that you actually always need it to optimise any and every task. A specific example is in this paper which states:

The Heisenberg limit is thus achieved without any entanglement between the arms of the interferometer. In fact, Jiang, Lang, and Caves [4] showed that the state ∣∣ψin⟩optis the only nonclassical product state, i.e., not a coherent state, that produces no modal entanglement after a beam splitter. These results indicate that, as in Ref. [18], modal entanglement is not a crucial resource for quantum-enhanced interferometry.

A basic but important research skill, 6: skepticism

Feynman said "The first principle is that you must not fool yourself and you are the easiest person to fool."

Walter Kauzmann emphasised that people will often believe what they want to believe rather than what the evidence before them suggests they should believe.

Students need to learn skepticism. Furthermore, it needs to be modelled to them by their advisors.
In particular, students should not just believe something because

- their advisor/supervisor believes it or tells them it is true
- it has been published, especially if it is in a luxury journal
- someone famous [or a group of famous people] claims it is true
- it is an exciting idea.

Basic but important questions to ask are:

What is the evidence? How reliable is the evidence?
Is there an alternative explanation, particularly a simpler one?

Maybe I am just becoming a grumpy old man, but I think I do increasingly encounter students and young researchers who lack this basic skill.
I fear that this is because of the seductive power of "sexy" explanations and topics. Furthermore, some of the students mentors and role models don't model or practise skepticism, particularly if their career success and funding [or hope thereof] depends on the exotica favoured by the luxury journals.

Good science is just plain hard work and not as exciting or clear cut as we might wish.

Calibrating a ruler for hydrogen bond lengths

I have just finished a paper with Bijyalaxmi Athokpam and Sai  Ramesh,
Isotopic fractionation in proteins as a measure of hydrogen bond length

If a deuterated molecule containing strong intramolecular hydrogen bonds is placed in a hydrogenated solvent it may preferentially exchange deuterium for hydrogen. This preference is due to the difference between the vibrational zero-point energy for hydrogen and deuterium.  It is found that the associated fractionation factor $\Phi$  is correlated with the strength of the intramolecular hydrogen bonds. This correlation has been used to determine the length of the H-bonds (donor-acceptor separation) in a diverse range of enzymes and has been argued to support the existence of short low-barrier H-bonds.

Starting with a potential energy surface based on a simple diabatic state model for H-bonds we calculate $\Phi$ as a function of the proton donor-acceptor distance $R$.  For numerical results, we use a parameterization of the model for symmetric O-H.... O bonds.  We consider the relative contributions of the O-H stretch vibration, O-H bend vibrations (both in plane and out of plane), tunnelling splitting effects at finite temperature, and the secondary geometric isotope effect. We
compare our total $\Phi$ as a function of $R$ with NMR experimental results for enzymes, and in particular with an empirical parametrisation $\Phi(R)$, used previously to determine bond lengths.

I welcome any comments or suggestions.

Declining universities

Universities (and their problems) are certainly increasingly in the news. Here are a few things I read recently and recommend. Unfortunately, a lot of it is discouraging.

The Economist ran a cover story The World is Going to University (but is it worth it?)  and special report. It particularly documents the "massification" that is going on and the associated problems. Did you know China has hired almost 100,000 new faculty in the past few decades!

UQ economist John Quiggin wrote an excellent piece Rank delusions in the (USA) Chronicle of Higher Education.
[If it is behind a pay-wall you can read it on his blog].
Basically annual university rankings are a pointless exercise that just tell us what we already know. They are actually basically the same as 100 years ago! In contrast, the top 50 companies on the Dow Jones index are completely different.

The eminent British literary critic Terry Eagleton has a biting piece The Slow Death of the University (also in the Chronicle). In the midst of the humorous and engaging rant about the state of British universities, a major and profound point is

the slow death of the university as a center of humane critique. Universities, which in Britain have an 800-year history, have traditionally been derided as ivory towers, and there was always some truth in the accusation. Yet the distance they established between themselves and society at large could prove enabling as well as disabling, allowing them to reflect on the values, goals, and interests of a social order too frenetically bound up in its own short-term practical pursuits to be capable of much self-criticism. Across the globe, that critical distance is now being diminished almost to nothing, as the institutions that produced Erasmus and John Milton, Einstein and Monty Python, capitulate to the hard-faced priorities of global capitalism...

Education should indeed be responsive to the needs of society. But this is not the same as regarding yourself as a service station for neocapitalism. In fact, you would tackle society’s needs a great deal more effectively were you to challenge this whole alienated model of learning... 

[The British government should] also seek to restore the honorable lineage of the university as one of the few arenas in modern society (another is the arts) in which prevailing ideologies can be submitted to some rigorous scrutiny. What if the value of the humanities lies not in the way they conform to such dominant notions, but in the fact that they don’t?

Aside: I really like Eagleton as a public intellectual. On my personal blog about theology, I have written several posts about him.

Ireland seems to be abandoning any basic research. Everything must have clear commercial benefits.

Tonight the Australian TV show Four Corners ABC [publicly funded channel] is running a story, Degrees of Deception about universities lowering academic standards in order to enrol and graduate mediocre international students who pay hefty tuitions. There is a related article in the Australian today (behind a paywall unless you Google "Education's double bind").

Teaching enhances research enhances teaching

This is the main point of a nice article by Roald Hoffmann, that I posted about in the early days of this blog.

I experienced this a few weeks ago. I have been working on a paper with my postdoc Nandan Pakhira about the viscosity of strongly correlated fermion fluids, focussing on the Hubbard model. A basic issue I got quite confused about is the relation between the momentum, Bloch wave vector, and velocity of an electron in a Bloch state. Yet, I when I taught this to my solid state physics class I was reminded of the correct result.

You really should turn off your email occasionally

I should too.
Last week I was on vacation at Bribie Island with my family.
[Aside: this is the location of my profile picture you can see to the right].

We stayed in a house with, thankfully, no internet access.
I don't have a phone.
I could have gone to the local library or to McDonalds to access the internet.
But, why spoil a good holiday?
I set up my email with an "out of office" auto-reply. When I came back to work 2 days ago I went through the 140 messages in about 20 minutes.
This was incredibly efficient.
Most were deleted. About a dozen were about science or some admin. tasks requiring action.
I set up one delayed post on my blog during my absence.

I survived. My colleagues survived. My students survived. My friends survived. My collaborators survived. Bureaucrats survived.
Most things can wait.

I benefited from not having the distraction or of thinking about things I would have to do when I got back.

I find a greater challenge is turning off email for a few hours during the day. I need to keep working on it.

Are American universities Crystal Cathedrals?

The documentary The Ivory Tower is worth watching.
It gives a broad balanced overview of the major challenges facing undergraduate education in the USA. The particular focus in on the sky-rocketing cost of tuition and student debt [now greater than $1 trillion]. It is alarming that since the 1970’s tuition has increased at a greater rate than any other “commodity”, even health care!

The documentary highlights that major contributions to the increasing cost are increasing number of administrators, many of excessive salaries, and fancy buildings [gyms, swimming pools, cafes, luxury apartments, …. all with lots of glass and open space] designed to lure students.
Rankings and status have played a perverse role leading to an unsustainable “arms race”.

But it is not all about affordability; attention is given to the other two vertices of the iron triangle [although that term is not used]: quality and access.
The hype and limited potential of MOOC’s is discussed.
They are no substitute for personal interaction, illustrated by “office hours” for the massive CS150 course at Harvard.

Andrew Delbanco features several times, emphasing the importance of quality, the intrinsic value of education [not just its monetary or utilitarian value], its role in personal transformation, specifically a broad liberal arts education, particularly in a  healthy democracy. Yet, he is no naive idealist, discussing the extreme pressures, contradictions, and instabilities of the current system.

The fascinating story of The Cooper Union is interspersed through the documentary, featuring the 60 day student occupation of the President's office.
It has now started charging tuition, contrary to the stated wishes of its founder, and its mission statement.
This dramatic change has been forced by financial mismanagement.
Cooper took out hundreds of millions dollar in loans to pay for a very fancy new building and to invest in hedge funds that lost a lot of money in the 2008 crash. The president is paid $700K per year plus a free multi-story apartment in New York City; just to lead an institution with 1000 students!

I am not sure “The Ivory Tower” is the appropriate title or metaphor.
To me  it may be The Crystal Cathedral: ostentatious, expensive, full of debt, and a perversion of what it should be?

I thank Stewart Gill for lending me a copy of the DVD. It is a pity the documentary is not available for free. But, that is a sign of how big the problem is. People are willing to pay money to watch a documentary about a depressing subject.

Superfluid helium on prime time TV

Unfortunately, The Big Bang Theory TV show features little physics these days. It is often just like "Friends" except some of the characters happen to work at Caltech. However, a recent episode, "The Troll Manisfestation" centred on superfluid helium and also mentions co-authorship, the arXiv, and physics blogs. There is some commentary on the physics in the episode by string theorist, Lubos Motl.

Effective tutorials, II.

I think one of the weakest aspects of my teaching is running tutorials. In Australia, for most upper level undergraduate courses there is a weekly one hour tutorial [problem solving session] that is run by the lecturer.

Mostly I have run these tutorials according to a traditional format. There are a set of problems that the students are meant to attempt before the session. At the tutorial I then work through the solutions on the board. There are many problems with this approach. Students often don't attempt the problems beforehand because they are not assessed. It is just like a lecture. Students are hesitant to ask questions and just write down what you write on the board. It is somewhat boring. I am not sure the students get much out of it.

Previously, I posted about a different approach that my colleague Joel Corney introduced for a large second year class we were co-teaching. I thought this was quite effective. But, it also required TA's (grad. student tutors) to help.

For PHYS4030 [a solid state physics class with 15 fourth year undergrads] I finally did something I have wanted to do for a long time. Each week I have assigned two students in the class to run the tutorial. They can opt out if they want. They are meant to attempt them beforehand. They then stand at the board and do what they can. Other students offer suggestions and ask questions. I only speak up when essential.

I think it is going well. The students seem more engaged.  Furthermore, it is very helpful for me to see what they find difficult or are confused about; sometimes things that I think are basic and gloss over too quickly. On the other hand, I think you do need a critical mass of motivated and engaged students. Unfortunately, not every class has this.

I welcome other ideas.

What does it mean to "observe" a Fermi surface?

The primary point of this post is to raise a philosophical question, "What is definitive experimental evidence for the existence of quasi-particles and a Fermi surface in a metal?"
Specifically, if one sees quantum oscillations, such as Shubnikov de Haas, or maps out the Fermi surface using Angle Dependent MagnetoResistance, has one "seen" the Fermi surface?

The secondary point is an unfortunate one. It provides another concrete example of the perverse influence of luxury journals, particularly the Nature Publishing Group, on science.
People make silly unjustified claims to get published.

At first I was excited when I saw the Nature Communications paper
Quasiparticles and Fermi liquid behaviour in an organic metal 
 T. Kiss, A. Chainani, H.M. Yamamoto, T. Miyazaki, T. Akimoto, T. Shimojima, K. Ishizaka, S. Watanabe, C.-T. Chen, A. Fukaya, R. Kato, S. Shin

It reports Angle Resolved PhotoEmission Spectroscopy (ARPES) measurements on an organic metal. For the last 20 years ARPES has been a workhorse for studying cuprate superconductors. However, organics seem to have been beyond its reach, partly because the crystals can be easily damaged by the high intensity X-rays used. When I give talks about organics people often ask about ARPES measurements. So, I thought perhaps finally the time had come.
The authors of the paper are to be commended for taking on this challenging task.

The abstract of the paper states

Many organic metals display exotic properties such as superconductivity, spin-charge separation and so on and have been described as quasi-one-dimensional Luttinger liquids. However, a genuine Fermi liquid behaviour with quasiparticles and Fermi surfaces have not been reported to date for any organic metal. Here, we report the experimental Fermi surface and band structure of an organic metal (BEDT-TTF)3Br(pBIB) obtained using angle-resolved photoelectron spectroscopy, and show its consistency with first-principles band structure calculations. Our results reveal a quasiparticle renormalization at low energy scales (effective mass m*=1.9 me) and ω² dependence of the imaginary part of the self energy, limited by a kink at ~50 meV arising from coupling to molecular vibrations. The study unambiguously proves that (BEDT-TTF)3Br(pBIB) is a quasi-2D organic Fermi liquid with a Fermi surface consistent with Shubnikov-de Haas results.

Then I looked at the actual data in the paper. Some is shown below.
It is rather noisy!
The lower figure shows the deduced Fermi surface on top of an ARPES intensity map.

Based on the quality of the data, I don't think it is appropriate to state "The study unambiguously proves that (BEDT-TTF)3Br(pBIB) is a quasi-2D organic Fermi liquid with a Fermi surface".

What do you think?

Prior to this paper there were Shubnikov de Haas measurements on the same material and Angle-Dependent MagnetoResistance, reported here. The data is shown below.

This is clean and impressive. Indeed the beating in the SdH and the peaks in ADMR at 90 degrees reflect that there is actually a coherent three-dimensional Fermi surface, a warped cylinder.

From the ADMR one can map out the intra-layer Fermi surface, using some theory, which assumes Fermi liquid quasi-particles. The result is below. The area is consistent with the frequency of SdH oscillations.

The authors neglect to mention this, even though they reference the paper that contains this figure. Furthermore, they make the extraordinary claim,

the present result constitutes the only case of an experimentally measured k-resolved Fermi surface of an organic metal. 

I am gobsmacked because in 1996 a book was published
Fermi Surfaces of Low-Dimensional Organic Metals and Superconductors by Joachim Wosnitza.
It contains multiple pictures of "experimentally measured k-resolved Fermi surfaces".

If you asked me "Does this material have a Fermi surface?" I would say, purely based on the ADMR that I was pretty confident it did.

Putting aside all the noisy data and hype, there is an important philosophical and scientific question,
"Is ARPES really a more fundamental measurement of or robust evidence for a Fermi surface than ADMR and SdH?"
There are some subtle issues here, as discussed here. For example, with a marginal Fermi liquid one can still get SdH.