Friday, December 2, 2016

A central result of non-equilibrium statistical physics

Here is a helpful quote from William Bialek. It is a footnote in a nice article, Perspectives on theory at the interface of physics and biology.
The Boltzmann distribution is the maximum entropy distribution consistent with knowing the mean energy, and this sometimes leads to confusion about maximum entropy methods as being equivalent to some sort of equilibrium assumption (which would be obviously wrong). But we can build maximum entropy models that hold many different expectation values fixed, and it is only when we fix the expectation value of the Hamiltonian that we are describing thermal equilibrium. What is useful is that maximum entropy models are equivalent to the Boltzmann distribution for some hypothetical system, and often this is a source of both intuition and calculational tools.
This type of approach features in the statistical mechanics of income distributions.

Examples where Bialek has applied this includes voting patterns of the USA Supreme Court, flocking of birds, and antibody diversity.

For a gentler introduction to this profound idea [which I still struggle with] see
*James Sethna's textbook, Entropy, Order parameters, and Complexity.
* review articles on large deviation theory by Hugo Touchette, such as this and this.
I thank David Limmer for bringing the latter to my attention.

Wednesday, November 30, 2016

Photosynthesis is incoherent

Beginning in 2007 luxury journals published some experimental papers making claims that quantum coherence was essential to photosynthesis. This was followed by a lot of theoretical papers claiming support. I was skeptical about these claims and in the first few years of this blog wrote several posts highlighting problems with the experiments, theory, interpretation, and hype.

Here is a recent paper that repeats one of the first experiments.

Nature does not rely on long-lived electronic quantum coherence for photosynthetic energy transfer Hong-Guang Duan, Valentyn I. Prokhorenko, Richard Cogdell, Khuram Ashraf, Amy L. Stevens, Michael Thorwart, R. J. Dwayne Miller
During the first steps of photosynthesis, the energy of impinging solar photons is transformed into electronic excitation energy of the light-harvesting biomolecular complexes. The subsequent energy transfer to the reaction center is understood in terms of exciton quasiparticles which move on a grid of biomolecular sites on typical time scales less than 100 femtoseconds (fs). Since the early days of quantum mechanics, this energy transfer is described as an incoherent Forster hopping with classical site occupation probabilities, but with quantum mechanically determined rate constants. This orthodox picture has been challenged by ultrafast optical spectroscopy experiments with the Fenna-Matthews-Olson protein in which interference oscillatory signals up to 1.5 picoseconds were reported and interpreted as direct evidence of exceptionally long-lived electronic quantum coherence. Here, we show that the optical 2D photon echo spectra of this complex at ambient temperature in aqueous solution do not provide evidence of any long-lived electronic quantum coherence, but confirm the orthodox view of rapidly decaying electronic quantum coherence on a time scale of 60 fs. Our results give no hint that electronic quantum coherence plays any biofunctional role in real photoactive biomolecular complexes. Since this natural energy transfer complex is rather small and has a structurally well defined protein with the distances between bacteriochlorophylls being comparable to other light-harvesting complexes, we anticipate that this finding is general and directly applies to even larger photoactive biomolecular complexes.
I do not find the 60 fsec timescale surprising. In 2008, Joel Gilmore and I published a review of experiment and theory on a wide range of biomolecules (in a warm wet environment) that suggested that tens of femtoseconds is the relevant time scale for decoherence.

I found the following section of the paper (page 7) interesting and troubling.
The results shown in Figs. 3 (a) and (b) prove that any electronic coherence vanishes within a dephasing time window of 60 fs. It is important to emphasize that the dephasing time determined like this is consistent with the dephasing time of Ď„hom = 60 fs independently derived from the experiment (see above). It is important to realize that this cross-check constitutes the simplest and most direct test for the electronic dephasing time in 2D spectra. In fact, the only unique observable in 2D pho- ton echo spectroscopy is the homogeneous lineshape. The use of rephasing processes in echo spectroscopies removes the inhomogeneous broadening and this can be directly inferred by the projection of the spectrum on the antidiagonal that shows the correlation between the excitation and probe fields. This check of self-consistency has not been made earlier and is in complete contradiction to the assertion made in earlier works. Moreover, our direct observation of the homogeneous line width is in agreement with independent FMO data of Ref. 12. This study finds an ∼ 100 cm−1 homogeneous line width estimated from the low-temperature data taken at 77 K, which corresponds to an electronic coherence time of ∼ 110 fs, in line with our result given the difference in temperature. In fact, if any long lived electronic coherences were operating on the 1 ps timescale as claimed previously (1), the antidiagonal line width would have to be on the order of 10 cm−1, and would appear as an extremely sharp ridge in the 2D inhomogeneously broadened spectrum (see Supplementary Materials). The lack of this feature conspicuously points to the misassignment of the long lived features to long lived electronic coherences where as now established in the present work is due to weak vibrational coherences. The frequencies of these oscillations, their lifetimes, and amplitudes all match those expected for molecular modes (41, 42) and not long-lived electronic coherences.

Monday, November 28, 2016

Polanyi and Emergence before "More is Different"

The common narrative in physics is that the limitations of reductionism, the importance of emergence, and the stratification of scientific fields and concepts were first highlighted in 1972,  by P.W. Anderson in a classic article, "More is Different" published in Science. Anderson nicely used broken symmetry as an example of an organising principle that occurs at one strata and as a result of the thermodynamic limit.

The article was based on lectures Anderson gave in 1967.
The article actually does not seem to contain the word "emergence". He talks about new properties "arising".

I recently learned how similar ideas about emergence and the stratification of fields was enunciated earlier by Michael Polanyi, in The Tacit Dimension, published in 1966, based on his 1962 Terry Lectures at Yale.
The book contains a chapter entitled "Emergence".

Here is a quote:
you cannot derive a vocabulary from phonetics; you cannot derive the grammar of language from its vocabulary; a correct use of grammar does not account for good style; and a good style does not provide the content of a piece of prose. ... it is impossible to represent the organizing principles of a higher level by the laws governing its isolated particulars.
Much of the chapter focuses on biology and the inadequacy of genetic reductionism. These ideas were expanded in a paper, "Life's irreducible structure," published in Science in 1968.

I recently learned about Polanyi's contribution from
The concept of emergence in social sciences: its history and importance 
G.M. Hodgson

Here is a bit of random background.

Before turning to philosophy, Polanyi worked very successfully in Physical Chemistry. Some readers will know him for his contributions to reaction rate theory, the transition state, a diabatic state description of proton transfer, the LEPS potential energy surface based on valence bond theory, ...

Polanyi was the Ph.D. advisor of Eugene Wigner. Melvin Calvin, a postdoc with Polanyi, and his son, John Polanyi, went on to win Nobel Prizes in Chemistry.

Google Scholar lists "The Tacit Dimension" with almost 25,000 citations.
The book was recently republished with a new foreword by Amartya Sen, Nobel Laureate in Economics.

Friday, November 25, 2016

Should you quit social media?

The New York Times has an interesting Op-ed. piece Quit Social Media. Your Career May Depend on It, by Cal Newport, a faculty member in computer science at Georgetown University.

When I saw the headline I thought the point was going to be an important one that has been made many times before; people sometimes post stupid stuff on social media and get fired as a result. Don't do it!
However, that is not his point.
Rather, he says social media is bad for two reasons:

1. It is a distraction that prevents deep thinking and sustained  "deep" work. Because you are constantly looking at your phone, tablet, or laptop or posting on it, you don't have the long periods of "quiet" time that are needed for substantial achievement.

2. Real substantial contributions will get noticed and recognised without you constantly "tweeting" or posting about what you are doing or have done. Cut back on the self-promotion.

Overall, I agree.

When I discussed this and my post about 13 hour days with two young scientists at an elite institution they said: "you really have no idea how much time some people are wasting on social media while in the lab." Ph.D students and postdocs may be physically present but not necessarily mentally or meaningfully engaged.

A similar argument for restraint, but with different motivations, is being advocated by Sherry Turkle, a psychologist at MIT. Here is a recent interview.

I welcome discussion.

Thursday, November 24, 2016

The many scales of emergence in the Haldane spin chain

The spin-1 antiferromagnetic Heisenberg chain provides a nice example of emergence in a quantum many-body system. Specifically, there are three distinct phenomena that emerge that were difficult to anticipate: the energy gap conjectured by Haldane, topological order, and the edge excitations with spin-1/2.

An interesting question is whether anyone could have ever predicted these from just knowing the atomic and crystal structure of a specific material. I suspect Laughlin and Pines would say no.

To understand the emergent properties one needs to derive effective Hamiltonians at several different length and energy scales. I have tried to capture this in the diagram below. In the vertical direction, the length scales get longer and the energy scales get smaller.


It is interesting that one can get the Haldane gap from the non-linear sigma model. However, it coarse grains too much and won't give the topological order or the edge excitations.

It seems to me that the profundity of the emergence that occurs at the different strata (length scales) is different. At the lower levels, the emergence is perhaps more "straightforward" and less surprising or less singular (in the sense of Berry).

Aside. I spend too much time making this figure in PowerPoint. Any suggestions on a quick and easy way to make such figures?

Any comments on the diagram would be appreciated.

Wednesday, November 23, 2016

How I got a Wikipedia page

It has dubious origins.

Some people are very impressed that I have a Wikipedia page.
I find this a bit embarrassing because there are many scientists, more distinguished than I, who do not have pages.
When people tell me how impressed they are I tell them the story.

Almost ten years ago some enthusiasts of "quantum biology" invited me to contribute a chapter to a book on the subject. The chapter I wrote, together with two students, was different from most of the other chapters because we focussed on realistic models and estimates for quantum decoherence in biomolecules. (Some of the material is here.) This leads one to be very skeptical about the whole notion that quantum coherence can play a significant role in biomolecular function, let alone biological processes. Most other authors are true believers.

I believe that to promote the book one of the editors had one of his Ph.D. students [who appeared to also do a some of the grunt work of the book editing] create a Wikipedia page for the book and for all of the senior authors. These pages emphasised the contribution to the book and the connection to quantum biology.

The "history" of my page states it was created by an account that
An editor has expressed a concern that this account may be a sock puppet of Bunzil (talk · contribs · logs).
I have since edited my page to remove links and references to the book since it is not something I want to be defined by.

An aside. Today I updated the page because when giving talks I got tired of sometimes being introduced based on outdated information on the page.

Hardly, a distinguished history....


The xkcd cartoon is from here.

Monday, November 21, 2016

The "twin" excited electronic state in strong hydrogen bonds

One of the key predictions of the diabatic state picture of hydrogen bonding is that there should be an excited electronic state (a twin state) which is the "anti-bonding" combination of the two diabatic states associated with the ground state H-bond.
Recently, I posted about a possible identification of this state in malonaldehyde.

The following recent paper is relevant.

Symmetry breaking in the axial symmetrical configurations of enolic propanedial, propanedithial, and propanediselenal: pseudo Jahn–Teller effect versus the resonance-assisted hydrogen bond theory
Elahe Jalali, Davood Nori-Shargh

The key figure is below. The lowest B2 state is the twin state.
In the diabatic state picture, Delta is half of the off-diagonal matrix element that couples the two diabatic states.
Similar diagrams occur when O is replaced with S or Se.



The paper does not discuss twin states, but interprets everything in terms of the framework of the
 (A1 + B2) ⊗ bpseudo-Jahn-Teller effect. 

Two minor issues might be raised about this work.
It uses TD-DFT (Time-dependent Density Functional Theory). It is contentious how reliable that is for excited states in organic molecules.
The diabatic states are not explicitly constructed.
These issues could be addressed by using higher level quantum chemistry and constructing the diabatic states by a systematic procedure, as was done by Seth Olsen for a family of methine dye molecules.