## Saturday, February 28, 2015

### Can you imagine a university president like this?

He gives away his whole salary to a not-for-profit.
He is reluctant to go into administration because he has to give up teaching.
He serves as president at the same institution for 35 years.
He increases the endowment from $9 million to$350 million.
When he takes over the university is mostly known for football. When he leaves it is a major research university.
He does not embrace the football program.
He introduces enrolment of female students.
He stands up to the president of the country over civil rights.
He is a major leader of campus opposition to a controversial war.
He changes the governance of the university so that it is no longer controlled by the sectarian founders, although he is one of them.
He speaks out often about issues of justice, human rights, racism, and poverty.
A survey of his peers identify him as the most effective college president in the country.

Is this fantasy? Could such a person actually exist?
But, this president is real.

Theodore Hesburgh, President of Notre Dame University in the USA, from 1952-1987.
He died last week, aged 97.
The New York Times obituary is worth reading.

## Friday, February 27, 2015

### In praise of modest goals

Maybe it is just my personality but I increasingly find that in science and life I am out of step with the surrounding culture. I just have modest goals.  I just want to understand a few things and make some sort of reliable contribution. This means publishing in PRB, J. Chem. Phys., and occasionally in PRL. I don't aspire to publish in luxury journals, double my funding, to see my university the most highly "ranked" in Australia, or claim that my research will revolutionise materials science and molecular biology, ...
This is why I increasingly find it hard and tedious to write grant applications.
I will also be happy if Liverpool just finish in the top 4 of the Premier League....

I think good science is really hard and most advances come from long term projects with painstaking hard work and from the occasional serendipity.

Yet it seems society is sold on hype, the winner takes all mentality, and everyone should aspire to be a winner...

I am certainly interested in big questions and grand challenges. But I feel I am realistic about what contributions I and others (even the extremely gifted and well funded) can make. It is generally the long slow road. Earlier I posted about how I am skeptical and left cold by "big hairy audacious goals".

Here are a few of my inter-related problems with many of the goals and ambitions I encounter.

1. Many I find simply unrealistic, either scientifically, politically, or economically.
Furthermore, when I look at the ambitious goals that were hyped 5, 10, 20, and 30 years ago I see they have failed.

2. Many, particularly young, people are left feeling like "failures" because they did not "succeed" by becoming the "best", e.g. by publishing in a luxury journal.

3. They divert resources (time, energy, money, and talent) away from modest goals that may produce more actual fruit in the long term.
I think MOOC's, topological insulators, string theory, AdS-CFT, topological quantum computing, iron-based superconductors .... are all interesting and worth a few select groups playing around with. But I fail to see the justification for hordes of people working on them.

4. They can easily degenerate into fantasy and hype.

5. Some of these ambitious enterprises become institutionalised to the point that defending the "vision" leads to propaganda and an unwillingness to listen to criticism and change course. Peter Woit's blog does a nice job of showing how this is the case for string theory. Here are two other examples, from social activism.
Teach for America has the laudable goal of attracting gifted and privileged graduates to teach in poorly resourced schools. However, an article documents the incredible lengths they go to in order to mute negative publicity.
Microfinance is a great initiative that helps alleviate poverty in the Majority world. However, when two MIT economists, the authors of Poor Economics, did a systematic study of its effects, they found that it produced modest but tangible benefits. Unfortunately, they were roundly attacked by some not-for-profits because the study contradicted their grand claims that microfinance was completely transforming the lives of recipients.

But, maybe it is just my personality ...

## Wednesday, February 25, 2015

### The beauty and mysteries of imaginary time and temperature

Yesterday, at UQ Robert Mann gave a nice Quantum Science seminar, "Hot and Cold Accelerating Detectors".

It concerned the Unruh effect: suppose one observer is constantly accelerating relative to another. Then, what is a quantum vacuum (for a free boson or fermion field) to one observer is a thermally populated state to the other.

Specifically, if one considers a field with wave vector k and energy Ω k. Then the expectation of the number operator is,
$\begin{array}{}\text{(5)}& ⟨0|{b}_{k}^{†}{b}_{k}|0⟩=\left({e}^{2\pi {\mathrm{\Omega }}_{k}/g}-1{\right)}^{-1},\end{array}$
which corresponds to a Bose distribution with a temperature given by
$\begin{array}{}& {T}_{\mathrm{U}\mathrm{n}\mathrm{r}\mathrm{u}\mathrm{h}}=\frac{g}{2\pi }=\frac{\hslash g}{2\pi c{k}_{B}}\end{array}$
where g is the constant acceleration. Note that this formula involves relativity (c), quantum physics (hbar), and statistical mechanics (kB).

I feel there is something rather profound going on here.
Without doing the calculation, it is perhaps not totally surprising that the accelerated observer sees a non-trivial occupation of excited states of the quantum field.
However, what is rather surprising to me is that the state occupation numbers has to be that associated with thermodynamic equilibrium.   Why not some other distribution? And that this holds for both fermions and bosons.
After all, you are starting purely with relativity [and the mathematics of Rindler co-ordinates] and quantum field theory and you are ending up with quantum statistical mechanics.

Is the thermal distribution just a "mathematical accident" because cosh functions are appearing in the Rindler co-ordinates, Bogoliubov transformation of the quantum field, and in thermal distribution?

The Scholarpedia page is helpful, stating this

can also be understood as a manifestation of the general relationship between temperature and imaginary time in quantum statistical mechanics (KMS theory). When t and τ are extended as complex variables, iτ is revealed as an angular variable in the (it,z) plane. The periodicity determined by g, the acceleration, is the only one that makes functions of τ be analytic in t. That period corresponds, under the KMS theory, to the reciprocal of the Unruh temperature (Dowker, 1978; Christensen and Duff, 1978; Sewell, 1982; Bell et al., 1985; Fulling and Ruijsenaars, 1987).''

I welcome any further elucidations on this rich and subtle issue.

## Monday, February 23, 2015

### Convincing correlations

Given the complexity of human subjects in economics, sociology, and medicine it is hard to find data that clearly indicates a correlation between two variables. I read The Economist each week and many of the graphs that they present just look like random noise to me. However, a year ago they showed the curves below, that I found rather convincing.

The graphs are in an article Tobacco and health: Where there's smoke that marked the fiftieth anniversary of the USA Surgeon Generals report which contained the graph on the left showing a correlation between life expectancy and smoking. The graph on the right shows how cigarette consumption in the USA has changed over time, reaching a maximum around the time of the report and decreasing after the banning of broadcast advertising.

Unfortunately, the response of tobacco companies to their reduces markets in affluent countries has been to shamelessly promote smoking in the Majority World and to intimidate those who oppose them. This humorous/disturbing video from John Oliver describes their antics. I was very proud to see that the previous Australian government led the way in standing up to the companies.

## Friday, February 20, 2015

### What does the Hubbard model miss?

How is a Hubbard model related to Density Functional Theory?

Jure Kokalj and I recently wrote a paper where considered the effect of strong correlations on thermal expansion, all within the framework of a Hubbard model. This is mostly concerned with explaining anomalies in organic charge transfer salts at temperatures less than 100 K, i.e. much less than the Fermi energy.

One referee stated
“However conceptually this Hamiltonian can not capture the free energy of the relevant electrons loyally. Recall the total energy decomposition in density functional theory, the Hamiltonian corresponds only to the band energy part (which is a summation of occupied Khon-Sham states and different from the kinetic energy) plus interaction term. And the remaining Hartree part, exchange-correlated part and also ionic part, which depend on the lattice constants, are totally ignored. It is not known whether the contributions from such terms are trivial or monotonic especially when strong correlation is present. The neglect of such terms in the electronic model in use is not justified. In this sense, even though the parameters are taken from first principles estimations, it is not surprising that the results are not consistent with experimental data quantitatively and sometimes even qualitatively."
There are some subtle issues here that I would like to understand.
I am not sure I fully understand the referee's comments.
And, I am not sure I agree.

1. Do I understand that the referee is suggesting that the Hubbard model does not include the effects contained in the Hartree and exchange correlation term? Surely, this is not correct.

2. I agree that the Hubbard model will be missing all effects associated with core electrons and ionic terms. However, surely any effects associated with these will not vary significantly on energy and temperature scales of the order of 100 K?

I welcome any comments and insight.

## Thursday, February 19, 2015

### Mapping quasi-particles in strongly interacting ultra cold fermionic gases

There is an interesting preprint
Breakdown of Fermi liquid description for strongly interacting fermions
Yoav Sagi, Tara E. Drake, Rabin Paudel, Roman Chapurin, Deborah S. Jin

It describes some nice ultra cold atom experiments that tune through the BEC-BCS crossover with a Feshbach resonance, focusing on the properties of the normal (i.e. non-superfluid) phase. All the measurements are at a temperature of T=0.2T_F, just above the superfluid transition.
It is like an ARPES [Angle Resolved PhotoEmission Spectroscopy] experiment in the solid state.
Specifically, the one-fermion spectral function A(k,E) is measured, shown in the colour intensity plots below.

The left and right side correspond to the BCS and BEC limits respectively. The unitary limit [i.e. infinite interaction occurs close to the middle].

On the left one can clearly see dispersing quasi-particle excitations, as one would expect in a Fermi liquid. As the interaction strength increases this feature is broader and there is more incoherent spectral weight at lower energies.

Some caution is in order as there is quite a bit of curve fitting involved in the analysis of the above data. [Solid state ARPES also suffers from this problem to.]

Specifically, the form below is used for the spectral function, where Z is the quasi-particle weight

In an earlier post I considered the history of this type of expression.

For the incoherent part the authors make the somewhat ad hoc assumption that it is given by a
"function that describes the normal state in the BEC limit, namely, a thermal gas of pairs."

They then find the following results for the dependence of Z and the effective mass m* [defined by the quadratic dispersion] on the interaction strength [a is the scattering length, which becomes infinite at the Feshbach resonance, i.e. for the unitary limit].
There is already a theory paper that discusses the experiments. It captures the results above at the semi-quantitative level using a Brueckner-Goldstone theory. The self energy is assumed to be frequency independent in this approximation. I found this interesting as it is the opposite to Dynamical Mean-Field Theory (DMFT) for which the self energy is assumed to be momentum independent.

I feel the paper title may be a misnomer. The quasi-particle weight is always finite, except in the BEC regime [attractive interactions] where one does not really have fermions anymore.

In future experiments, it would be nice to see the temperature dependence of the spectral function. Specifically, do the quasi-particles get destroyed with increasing temperature as in bad metals.

I thank Matt Davis for bringing the preprint to my attention.

## Wednesday, February 18, 2015

### The case against citation metrics

This year I am on a committee that looks at funding applications from all areas of science. Inevitably, this will lead to problematic comparisons of the track records of mathematicians versus physicists versus biologists. The quick, lazy, and unjustified recourse is to start invoking impact factors and publications in luxury journals.

There is a very thorough and helpful report Citation Statistics from the International Mathematical Union that clearly shows how problematic citation metrics are.
Of particular interest is the graph below.
Note that mathematicians are cited three times less than physicists and six times less than life scientists.

Aside: I am not clear what the distinction is between life sciences and biological sciences. Is the latter more oriented to humans [e.g. medicine] and the latter plants and animals?

This report is cited in the San Francisco Declaration on Research Assessment, initiated by biologists, that is attracting significant interest and mentioned by Carl Caves on High Impact Factor Syndrome.