Thursday, March 26, 2015

A basic but important research skill, 5: solving homework problems

Carl Caves has a helpful two pager, tips for solving physics homework problems. It nicely emphasises the importance of drawing a clear diagram, dimensional analysis, thinking before you calculate, and checking the answer.

He also discusses moving from homework problems to "real world" problems, e.g. research. Then, just formulating the problem is crucial.

I wonder if the goals of some Ph.D projects might be revised if the supervisor and/or student simply combined dimensional analysis with a realistic order of magnitude estimate. Just doing the exercise might also significantly increase the students understanding of the underlying physics.

Wednesday, March 25, 2015

Enhanced teaching of crystal structures

This past week I taught my condensed matter class about crystal structures and their determination by X-rays. This can be a little dry and old. Here, are few things I do to try and make things more interesting and relevant. I emphasise that many of these developments go beyond what was known or anticipated when Ashcroft and Mermin was written. Furthermore, significant challenges remain.

Discuss whether the first X-ray crystallography experiment the most important experiment in condensed matter, ever?

Take crystal structure "ball and stick" models to the lectures.

Give a whole lecture on quasi-crystals.

Use the bravais program in Solid State Simulations to illustrate basic ideas. For example, the equivalence of each reciprocal lattice vector to an X-ray diffraction peak, to a family of lattice planes in real space, and to a Miller indice.

Show a crystal structure for a high-Tc cuprate superconductor and an organic charge transfer salt. Emphasize the large number of atoms per unit cell and how small changes in distances can totally change the ground state (e.g. superconductor to Mott insulator). Furthermore, these small changes may be currently beyond experimental resolution. This is very relevant to my research and that of Ben Powell.

Very briefly mention the Protein Data Bank, and its exponential growth over the past few decades. It now contains more than 100,000 bio-molecular structures. Mention the key concept that Structure determines Property determines Function. Mention that although many structures resolve bond lengths to within 0.2-0.6 Angstroms, that this just isn't good enough to resolve some important questions about chemical mechanisms related to function. I am currently writing a paper on an alternative "ruler" using isotopic fractionation. 

Next year I may something about the importance of synchrotrons and neutron sources, and crystallographic databases such as the Cambridge Structural Database, which contains more than 700,000 structures for small organic molecules and organometallics.

Tuesday, March 24, 2015

Is liquid 3He close to a Mott-Hubbard insulator transition?

Is it ever a "bad metal"?

Liquid 3He mostly gets attention because at low temperatures it is a Fermi liquid [indeed it was the inspiration for Landau's theory] and because it becomes a superfluid [with all sorts of broken symmetries].

How strong are the interactions? How "renormalised" are the quasi-particles?
The effective mass of the quasi-particles [as deduced from the specific heat] is about 3 times the bare mass at 0 bar pressure and increases to 6 times at 33 bar, when it becomes solid. The compressibility is also renormalised and decreases significantly with increasing pressure, as shown below.

This led Anderson and Brinkman to propose that 3He was an "almost localised" Fermi liquid. Thirty years ago, Dieter Vollhardt worked this idea out in detail, considering how these properties might be described by a lattice gas mode with a Hubbard Hamiltonian. The system is at half filling with U increasing with pressure, and the solidification transition (complete localisation of the fermions) having some connection to the Mott transition. All his calculations were at the level of the Gutzwiller approximation (equivalent to slave bosons). [The figure above is taken from his paper].
A significant result from the theory is it describes the weak pressure dependence and value of the Sommerfeld-Wilson ratio [which is related to the Fermi liquid parameter F_0^a].
At ambient pressure U is about 80 per cent of the critical value for the Mott transition.

Vollhardt, Wolfle, and Anderson also considered a more realistic situation where the system is not at half-filling. Then, the doping is determined by the ratio of the molar volume of the liquid to the molar volume of the solid [which by definition corresponds to half filling].

Later Georges and Laloux argued 3He is a Mott-Stoner liquid, i.e. one also needs to take into account the exchange interaction and proximity to a Stoner ferromagnetic instability.

If this Mott-Hubbard picture is valid then one should also see a crossover from a Fermi liquid to a "bad metal" with increasing temperature. Specifically, above some "coherence" temperature T_coh, the quasi-particle picture breaks down. For example, the specific heat should increase linearly with temperature up to a value of order R (the ideal gas constant) around T_coh, and then decrease with increasing temperature.

Indeed one does see this crossover in the experimental data shown in the figure below, taken from here.

Aside: the crossing point in the family of curves is an example of an isosbestic point.

Extension of the Vollhardt theory to finite temperatures was done by Seiler, Gros, Rice, Ueda, and Vollhardt.

One can also consider 3He in two dimensions. John Saunders and his group have done a beautiful series of experiments on monolayers and bilayers of 3He. The data below is for a monolayer, of different layer densities, taken from here. They suggest that as one tunes the density one moves closer to the Mott transition.

The experiments on bilayers deserve a separate post.

Monday, March 23, 2015

Two new books on career advice for Ph.Ds

The Professor Is In: The Essential Guide To Turning Your Ph.D. Into a Job by Karen Kelsky.
The author left a tenured position at a research university and now has an excellent blog and runs a career advice consulting business, for people in academia, both those who want to stay and those who want to (or have to) leave.

Navigating the Path to Industry: A Hiring Manager's Advice for Academics Looking for a Job in Industry by M.R. Nelson

Has anyone read either book? I welcome comments.

Saturday, March 21, 2015

The teaching bag

When I started teaching sometimes I would arrive at the lecture to find that I left behind something I needed (chalk!, laser pointer, computer connector, textbook, notes, ...).
Do I go back to my office and get it and start the lecture late, or do without?
Sometimes these are things that should be in the room but are not. (e.g. chalk, erasers, or markers).
Even worse was to discover I was missing something in the middle of the lecture!

I eventually came up with a simple solution. Have a separate bag in which I store absolutely everything I need or may need (white board markers, eraser, Mac adapters, text, clicker receiver, course profile, ....)
When I leave for the lecture I don't have to remember or find all these things.
For things like Mac adapters I have an extra one just for the bag.

It is a simple thing but it does reduce anxiety and problems.

Friday, March 20, 2015

Physicists are bosons; mathematicians are fermions

The first observation is that each mathematician is a special case, and in general mathematicians tend to behave like “fermions” i.e. avoid working in areas which are too trendy whereas physicists behave a lot more like “bosons” which coalesce in large packs and are often “over-selling” their doings, an attitude which mathematicians despise.
Alain Connes, Advice to beginning mathematicians

I learnt this quote today, courtesy of Elena Ostrovskaya, who gave todays Physics Colloquium at UQ.

Wednesday, March 18, 2015

An alternative to cosmic inflation

On Friday Robert Mann gave a very nice colloquium at UQ, The Black Hole at the Beginning of Time. The video is below.

The (end of) the talk is based on the recent paper
Out of the white hole: a holographic origin for the Big Bang 
Razieh Pourhasan, Niayesh Afshordi, and Robert B. Mann

The key idea is to consider our universe as the 4-dimensional boundary (brane or hologram) of a 5-dimensional space-time in which there is a black hole.
In our universe one then has not just 4D gravity and matter, but also induced gravity and an effective fluid from the 5D "bulk".

(For better or worse) this work was recently featured on the cover of Scientific American.

Robert covered a massive amount of material moving through special relativity, general relativity, black holes, big bang, cosmology, recent results from the Planck satellite,  inflation, the multiverse,... and finally his alternative model.
I took several pages of notes.
He went overtime. I think this was one of the rare cases where I did not mind the speaker doing it.

Besides learning some interesting physics, what was most interesting to me was the refreshing way the work was presented. The tone was something like, "cosmology has some amazing successes but there are a few paradoxes, inflation is an interesting idea but also presents some problems, ...fine tuning is a challenge, ... so let me throw out a different idea.... it is a bit weird... but lets see where it goes ... it also has some strengths and weaknesses .... I am not sure this is better than inflation, but it is worth looking at." There was no hype or sweeping things under the rug.

Many in the audience were undergrads. I thought it was a great talk for them to hear. It was largely tutorial, there was some fascinating physics, connections to experiment were emphasised, healthy skepticism was modelled, and there was no hype.

I also liked the talk because it confirms my prejudice that people need to work harder, more creatively, and more critically, on foundational problems in cosmology. Dark matter, dark energy, inflation, and fine tuning are all really weird. They may be right. But they may not be. I think just accepting them as the only option and regressing to even weirder ideas like the multiverse is a mistake. [Of course, it is easy as an outsider to tell colleagues to work harder and more creatively.]

The physical model of the early universe that was presented was completely different to inflation. Yet it solves most of the same problems (horizon, flatness, and no monopoles). Its biggest problem is that it does not predict the observed 4 per cent deviation from scale invariance.

The most important and interesting bits are from about 52:00 to 58:00.