Hydrogen bonds fluctuate like crazy

When I was in Slovenia a few weeks ago I spent a nice afternoon at the National Institute of Chemistry discussing hydrogen bond dynamics and spectroscopy with Jernez Stare and Joze Grdadolnik.

Janez Mavri was busy fielding phone calls from the press about his collaborator Ariel Warshel who had been awarded the Nobel Prize in Chemistry the previous day. I also met Dusan Hadzi, who was a real pioneer in hydrogen bond studies. He is now 92 years old but still comes into the lab each day, and is working on a several papers with younger collaborators!

Of particular interest are the Car-Parrinello simulations of sodium hydrogen bissulfate performed by Gordana Pirc, Stare, and Mavri.
This crystal has an O...O distance of R=2.432 Angstroms with slightly asymmetric O-H distances of r=1.156 and 1.276 A.
The Car-Parrinello runs show R fluctuating between 2.24 and 2.69 A!
Snapshots of the associated one-dimensional potentials for the OH stretch are shown below.

For each potential they solve the vibrational Schrodinger equation and calculate the associated OH stretching transition frequency. This then leads to frequency distribution and the infrared absorption line shape shown below.

Similar fluctuations [both thermal and quantum] occur in water but that is another story.

Getting an elephants trunk to wiggle II

Enrico Fermi told Freeman Dyson "with four parameters I can fit an elephant, and with five I can make him wiggle his trunk".

Phil Nelson kindly brought to my attention a nice paper
Drawing an elephant with four complex parameters
by Jürgen Mayer, Khaled Khairy, and Jonathon Howard

There is also an interactive Mathematica Demonstration that allows you to see how the quality of the fit increases with the number of parameters [but does not have a wiggling trunk!].

Quantum emergence is not strong emergence

Is there any difference in the nature of emergence in quantum and classical systems?
What is the difference between strong and weak emergence?

An emergent property of a system is one that is:
a. not present in the individual components of the system
b. difficult to predict a priori from a knowledge of the components and their interactions
c. independent of the finer details of the components

Equivalently emergent properties are
a. qualitatively different
b. usually discovered empirically and sometimes are given a reductionist explanation a posteriori
c. universal and stable to perturbations

This can be illustrated with the rigidity of a solid
a. the individual atoms that make up a solid are not rigid.
b. elasticity theory preceded crystallography
c. all solids are rigid, regardless of their chemical composition.

Emergence occurs in both quantum and classical systems.  The properties that emerge can be distinctly different.  Superconductivity  and superfluidity are intrinsically quantum.
However, the associated issues and challenges: scientific, methodological, and philosophical are essentially the same. Emergence in classical systems is just as fascinating and challenging as for quantum systems.

Hence, last year I was surprised and disappointed to read the details of The Physics of Emergence program at the Templeton Foundation.
It appears to be based on two significant misunderstandings:
Emergence in quantum and classical systems is profoundly different.
In particular, quantum and classical emergence should be identified with strong and weak emergence, respectively.
I disagree with both the preceding two statements.

What is the difference between strong and weak emergence?
Some philosophers equate these with ontological and epistemological emergence.
For practical scientists the issue boils down to the following possible
answers to the question, "Is it possible to predict emergent properties?":
i. No. It is impossible.
ii. No. But, one can make postdictions, i.e., once the phenomena has been observed very smart people can construct reductionist models that explain the phenomena.  [BCS theory is an example].
iii. Yes. But, it is difficult. BECs and topological insulators give us hope.
iv. Yes. We just need a little more computer power and creativity.

The believer in strong emergence says i. All the other answers amount to weak emergence.
Different scientists will answer ii, iii, or iv.
I would probably go with ii.
The only scientist who I think might answer i. is Bob Laughlin on his more cantankerous days.
Yet i. appears to be serious option for many philosophers. This seems to be largely because of the thorny issue of consciousness.

Science is broken

Science is all about creating reliable and reproducible knowledge.
The Economist has a cover story How science goes wrong.
It is worth reading, pondering, and discussing.

I agree with the general observations of the article. Unfortunately, some of my worst fears are confirmed. Some of the problematic issues that are highlighted have been discussed on this blog before. Problems discussed include:

• the career pressure to publish leading to a lot of low quality work
• the pre-occupation with "sexy"new results that can be published in high profile journals
• poor quality of refereeing, meaning many erroneous papers get published
• there are few papers about negative results because they are hard to get published
• there are few papers testing/confirming the results in other papers because they attract little attention

I like the article because it is constructive in proposing reform, particularly from within science, and does discuss various initiatives, including some funded by private foundations to address the problems. The article is not "anti-science", does not lead to postmodern conclusions, or suggesting cutting science funding.

I welcome discussion about the scope of these problems and ways we can address them.

Universal? properties of thermoelectric power in bad metals

There is a nice preprint Universal thermopower of bad metals
Veljko Zlatic, G.R. Boyd, Jim Freericks

It contains calculations of the temperature and doping dependence of the thermoelectric power for the Falicov-Kimball model within the approximation of Dynamical-Mean Theory [DMFT].

This spinless fermion model is even "simpler" than the Hubbard model. Yet it captures some of the same physics, particularly the Mott metal-insulator transition. It also has the advantage that DMFT has an exact analytical solution. One does not need an "impurity solver", such as for the Hubbard model. There is an extensive Rev. Mod. Phys. on this, by Freericks and Zlatic.

Below I discuss one significant disadvantage of the model.

The figure below shows the calculated temperature dependence of the thermopower for several different dopings. The solid lines are the result from the Kubo formula [essentially exact] and the dashed line is the approximate Kelvin formula [the derivative of the chemical potential with respect to temperature].

Note that both the magnitude [of order k_B/e=80 microVolt/K] and non-monotonic temperature dependence are similar to what one sees in many strongly correlated electron materials. [Compare for example this post about heavy fermion compounds.]

Furthermore, it is striking that the Kelvin formula gives semi-quantitative results that are reliable.

However, when it comes to detailed comparison with experiment on actual materials, it is important to keep in mind a significant shortcoming of the Falicov-Kimball model. It does not seem to have a low-energy coherence scale associated with the formation of Fermi liquid quasi-particles. In many strongly correlated electron materials this energy scale is much less than the bare energy scale t, of the intersite hopping. In the Figure above one can see that the temperature dependence of the thermopower occurs on a scale of order some significant fraction of the hopping t. For example, in organic charge transfer salts this is of order 400 K, and in the cuprates t is of order 4000 K. In these materials the thermopower varies on a scale that is one order of magnitude smaller.

I thank Nandan Pakhira for bringing the preprint to my attention.

90th Birthday conference for Phil Anderson

If there is any one individual who has influenced both the scientific content and philosophy of this blog it is Phil Anderson. There are 45 posts with "P.W. Anderson" as a label, more than any other individual. However, his influence goes far beyond that.

In December Princeton will host a 90th birthday celebration conference in his honour.

Belgrade bad metal talk

On thursday I am giving a seminar at the Institute of Physics in Belgrade, Serbia.
My host is Darko Tanasković. He recently did some nice work with Jaksa Vučičević, Hanna Terletska, and Vlad Dobrosavljević showing quantum critical scaling of the resistivity near the critical point of the Mott transition in Dynamical Mean-Field Theory [DMFT] of the half-filled Hubbard model. A recent PRB describes this in terms of a quantum Widom line.

Here is the current version of the slides for my talk.

In preparing the talk I realised that in some recent versions of this talk I did not includes a slide, "Open questions and future work." That is bad. Perhaps every talk should have such a slide. I want other people to work on problems I am working on and certainly don't want to create the impression that my recent work [on any topic] has "solved" the problem and there is not much left to do.