Rudolph Marcus (1923-2026): theoretical chemical physicist

Rudolph Marcus died last week. He was 102. There is a nice obituary in The New York Times. He was best known for his theory of electron transfer, for which he was the sole recipient of the Nobel Prize in Chemistry in 1992.

Although the theory was proposed for electron transfer in a polar solvent it applies to a wide range of other systems, where two quantum states are coupled to one another and to an environment. One example is for Forster transfer of excitons between molecules, which is central to photosynthesis.

I will give a physics perspective, based on a talk I gave in Slovenia back in 2013. Slides are here.

Basically, Marcus proposed an effective Hamiltonian for two diabatic states and calculated a transition rate in a limit that is relevant to most chemical contexts.

The Hamiltonian can be viewed as the spin-boson model, in which a two-level system is coupled to a bath of harmonic oscillators. 

[The dense book by Weiss on Quantum Dissipative Systems makes the connection explicit in detail. A more accessible treatment may be chapter 16 in the book Chemical Dynamics in Condensed Phases by Nitzan.]

The Hamiltonian is 

This defines a spectral density, which is important for quantum decoherence, but not so much here, except it defines a timescale that determines the classical limit, which Marcus assumed.

This can be used to define a quantity central to Marcus' theory, the reorganisation energy.

The transition rate between the two quantum states is given by

I consider this to be one of the most important equations in chemical physics, particularly for the understanding and design of functional materials.

Aside. Much of this is equivalent to Holstein's 1959 treatment of incoherent polaron transport (see Mahan, Many-body physics).

A key experiment by John R. Miller, Lidia T. Calcaterra and Gerhard L. Closs in 1984 showed how good the theory was and how its predictions were counter-intuitive. The authors considered a family of molecules that allowed them to tune epsilon, the energy difference between the two electronic states. [On the graph below epsilon = - Delta G].

The vertical scale is the reaction rate on a logarithmic scale. It varies by four orders of magnitude.

What is surprising? As stated at the Nobel prize award ceremony:

"The quadratic equation predicts that electron transfer reactions will occur more slowly the larger the driving force of the reaction is. This phenomenon received its own name, “the inverted region.” To a chemist, the phenomenon is just as unexpected as when a skier finds himself gliding more slowly down a slope the steeper it is."

The theory implies an important design principle for functional materials: if optimising functionality means maximising the reaction rate, then tune the energy difference epsilon to equal the reorganisation energy E_R.

The theory illustrates two important aspects of emergence: effective theories and universality. Many different systems can be described by the same theory. The environment may involve many degrees of freedom and its coupling to the system is characterised by many parameters (the M_alpha above). However, only one parameter matters, the reorganisation energy.

For Australians, there is some ambivalence about the way Marcus' name is often solely associated with electron transfer theory. We often refer to it as Marcus-Hush or Hush-Marcus theory because Noel Hush did similar work around the same time. Some of the history is recounted here by Ian Rae and Jeff Reimers. There are also subtle debates about whether the electron transfer is adiabatic or non-adiabatic.

My only personal interaction with Marcus was in 2011 when I visited the chemistry department at Caltech. Marcus kindly took me to lunch at the faculty club, along with his research group. Then he was 84 years old. He kept publishing papers until he died.

Philosophical perspectives on the emergence of molecular structure

 In philosophical discussions of emergence and reductionism in chemistry, molecular structure has received significant attention and debate. Sometimes molecular structure is used to justify strong emergence, i.e., that molecular cannot be predicted, even in principle, solely from quantum theory.

Primas was one of the first to claim that molecular structure could not be reduced to quantum physics. Consider the following statements.

“From a physical point of view the crucial point of a Born–Oppenheimer description is not a simplification of the mathematical problem, but the replacement of the basic theory by a related but qualitatively new one…

[the structure of benzene] does not exist in a full quantum-theoretical description since electrons and nuclei are entangled by Einstein-Podolsky–Rosen correlations. The concept of molecular structure does not follow from first principles - all molecules with the same empirical formula have the same Schrödinger equation, so that, at this level, the shape of a molecule as the main feature of molecular chemistry is simply not in evidence. In a quantum theoretical description the molecular shape emerges by abstracting from the actually existing Einstein-Podolsky–Rosen correlations between the electrons and the nuclei. Historically, the structure concept has been introduced into quantum chemistry by the so called Born-Oppenheimer approximation. But this terminology is misleading since the main issue is not an approximation, but the breaking of a holistic symmetry.”

I have italicised claims that are contestable and that I will discuss further below.

Cartwright has given philosophical arguments as to why chemistry cannot be reduced to physics. In this context, she claims (pp. 106-7)

“The typical method of quantum-mechanical treatment of molecules begins with the Born–Oppenheimer approximation…

This approximation treats the atomic nucleus as a classical particle. But this fundamentally violates quantum mechanics which, following the Heisenberg uncertainty principle, maintains that we cannot have a simultaneous assignment of fixed positions and fixed momenta. The approximations that provide the reduction violate the very theory that the chemistry is being reduced to… the success of quantum chemistry relies fundamentally on assumptions that belong to classical chemistry.” 

This claim that the BOA violates the Heisenberg uncertainty principle was rebutted in an earlier post and discussed in more detail by Huggett et al. Nevertheless, Lombardi et al. are not satisfied by the rebuttal.

Hendry claimed molecular structure is evidence of strong emergence and/or downward causation. In a similar spirit, Ellis and Drossel argued that crystal structures in solid state physics are evidence of strong emergence. The arguments of Hendry have been criticised by Seifert. The arguments centre around the fact that the molecular structure is a classical entity and a concept that is imposed, whereas a logically self-consistent approach would treat both electrons and nuclei quantum mechanically. It is claimed that the existence of molecular structures is assumed and not derived in quantum chemistry calculations as they assume the Born-Oppenheimer approximation (BOA). 

Scerri responded to these arguments claiming that chemistry (particularly the concept of molecular structure) is irreducible to quantum physics. He claimed these arguments are not valid because they misunderstand the role of the BOA. It does not violate the uncertainty principle and in practice chemists can and do perform non-BOA approximations. 

Fortin et al. rejected the view that decoherence can explain isomerism, as decoherence does not resolve issues associated with the quantum measurement problem. 

Franklin and Seifert claim “the problem of molecular structure just is the quantum measurement problem.” This is debatable. Most molecular structures can be understood in terms of the nuclear probability density having a unique maximum and decoherence then is not relevant. Decoherence and the collapse of the nuclear wavefunction are only relevant in systems such as ammonia and stereoisomers in which there are molecular structures with equal energy and separated by high energy barriers.

I now respond to some of the contestable claims of Primas.

“electrons and nuclei are entangled by Einstein-Podolsky–Rosen correlations”

It is possible to quantify and calculate the amount of entanglement between electrons and nuclei in a specific quantum state. In an EPR state the entanglement is maximal. In the BOA wavefunction entanglement is present, but is absent in the crude BOA. The entanglement has been estimated in benzene and is very small. The only molecules where the entanglement may be significant are those, such as isomers, where there are two degenerate molecular structures and the overlap of the associated nuclear wavefunctions is small (i.e., the tunnel splitting is small). But then, in most chemical situations decoherence will wash out this entanglement.

“all molecules with the same empirical formula have the same Schrödinger equation, so that, at this level, the shape of a molecule as the main feature of molecular chemistry is simply not in evidence.”

This is the problem of isomers. It is resolved because isomers are present in the solution to the Schrödinger equation, as I argued earlier.

“the crucial point of a Born–Oppenheimer description is not a simplification of the mathematical problem, but the replacement of the basic theory by a related but qualitatively new one… the main issue is not an approximation, but the breaking of a holistic symmetry.”

This seems subjective to me. I see the BOA as just a well-justified approximation. The electrons and nuclei are treated differently because they are. They have vastly different masses and this affects how they can be treated in any solution to the full Hamiltonian. Nevertheless, the BOA is a quantum theory and the nuclei are described by a wavefunction.

As discussed earlier, for small molecules in practise it is no longer necessary to use the BOA and the electrons and nuclei can be treated on an equal footing. Molecular structure is present in solutions to the full Schrödinger equation.

I wonder if the objection to use of the BOA is any different to the use of approximations in other theories? For example, consider theoretical treatments of the motion of planets in the solar system. The effects of all the planets are not treated on an equal footing. The effect of other planets on a planet of interest are treated perturbatively.

In conclusion, the arguments that molecular structure is evidence of strong emergence are weak. Some confusion may partly arise from misinterpreting the significance of the following valid observations.

i. Molecular structures were first conjectured before quantum theory was proposed.

ii. The BOA was proposed to explain molecular structure from quantum theory.

iii. Today, almost all calculations of molecular structure assume BOA.

iv. Chemists talk about molecular structures largely in classical not quantum terms.

However, the scientific reality is that for small molecules their structure, can be understood, described, and calculated in purely quantum terms. Yet, that understanding provides a strong justification for the validity of the BOA and for the convenience of using classical language to describe molecular structure.

I stress that the weakness of the arguments for the strong emergence of molecular structure, does not mean that an emergent perspective is not relevant to chemistry. Molecular structure is emergent, when defined in terms of novelty. This leads to effective theories defined in terms of potential energy surfaces. Furthermore, as the next section argues chemistry exhibits novel properties, concepts, and theories that are not present in physics.

This post is extracted from Section 15, of my review article "Emergence: from physics to biology, sociology, and computer science."

Are chemical isomers emergent?

In discussions of emergence, particularly in chemistry, isomers are often given as an example of an emergent phenomenon. In Anderson's original "More is Different" article, he discussed the chirality of sugar molecules as an example of symmetry breaking. More recently, isomers (and the associated concept of molecular structure) are invoked to justify contentious claims about strong emergence and downward causality.

Here, I explain what isomers are and consider whether they are emergent in the sense of novelty, i.e., they have properties that are qualitatively different from their constituents.

In a later post, I hope to address the more general and knotty problems of molecular structure and the Born-Oppenheimer approximation.

Structural isomers

These occur when a specific collection of atoms (chemical formula) can have more than one molecular structure. An example, shown below, is C3H4.

Each structure has different chemical and physical properties. Aggregates of each molecule can have different properties such as boiling and melting points.

Some isomers are more stable than others. They may be able to interconvert, but sometimes not on laboratory time scales.

From the point of view of a ground state potential energy surface, the different isomer structures correspond to different local minima on the surface.

Stereoisomers

The simplest example is HFClBr. There are two stable structures shown below. They are related by a chiral (mirror) symmetry. They differ physically in that they rotate the plane of polarisation of incident light in opposite directions. 

The isomers, known as enantiomers, have the same ground state energy. In terms of a potential energy surface, they correspond to two different minima and are separated by a high-energy barrier. In principle, the two forms can quantum-tunnel between each other.

Chemically, the two isomers differ in how they react with other chiral molecules.

Chirality is central to molecular biology. Proteins are made of amino acids, and in nature they all have the L-form. Most forms of DNA involve double helices with right-handed chirality. 

The chirality of drug molecules matters, as tragically found with thalidomide in the 1950s. 

Emergence?

The constituent components of these molecules can be viewed as electrons and atomic nuclei. Alternatively, the components could be viewed as the atoms they are made of. In both cases, the parts of the system do not have the structure and properties that the system does. The atoms, nuclei, and electrons all have spherical symmetry, whereas the molecules do not. Another argument is that since the isomers are qualitatively different from one another, at least one of them must be qualitatively different from the components. Hence, these molecular structures can be viewed as emergent.

However, this goes against the view that we generally associate emergence with systems with many interacting parts. If we take two massive particles interacting by gravity, they can form a stable orbit. Neither particle has this property, but we don't generally claim that such orbits are emergent.

[I am grateful to a commenter on an old post who pointed this out].

Isomers illustrate the diversity of forms often associated with emergence.

There are subtleties associated with the stability of enantiomers and the associated breaking of chiral symmetry. This is similar to the issue of ammonia having a stable pyramidal structure. (Also discussed by Anderson in "More is Different"). An isolated molecule in a vacuum will have no chirality. The ground state is a quantum superposition of both enantiomers. However, in the laboratory, the interaction of each molecule with its environment, such as other molecules, leads to decoherence that prevents quantum tunnelling. In that case, there are an infinite number of degrees of freedom associated with the environment, and they are crucial for the emergence of enantiomers.

Tony Leggett (1938-2026): condensed matter theorist

Tony Leggett died last week. The New York Times has a nice obituary. One measure of his influence on me is that more than 20 posts on this blog feature his work. He received the Nobel Prize in 2003 for developing the theory of superfluid 3He.

In 1972, a graduate student at Cornell, Doug Osheroff, discovered a phase transition around a temperature of 2 mK in liquid 3He. In the 1960s liquid 3He was established to be a Fermi liquid that was beautifully described by Landau's theory. Osheroff and his advisors, David Lee and Robert Richardson, incorrectly identified the phase transition as arising from antiferromagnetic order in the solid phase of 3He.

However, Leggett argued that it was actually due to superfluidity that there were two distinct superfluid phases, A and B, with different order parameters. 

Lee, Osheroff, and Richardson shared the Nobel Prize in 1996 for their discovery.

Leggett was primed to make rapid progress, as in 1965 and 1966 he had written three papers about superfluidity in liquid 3He, albeit assuming s-wave pairing. Indeed, by 1975 he wrote a comprehensive review article on the two superfluid phases.

For many reasons superfluid 3He was significant for the broader field of condensed matter. BCS showed that in elemental metals, superconductivity resulted from Cooper pairing of electrons due to an attractive electron-phonon interaction.  The order parameter (Cooper pair wave function) had s-wave spin singlet symmetry.

In contrast, superfluid 3He showed that Cooper pairing could also occur in a neutral Fermi liquid, and have non-trivial symmetry, i.e., p-wave symmetry and spin triplet. The order parameter has 18 components, compared to only 2 for elemental superconductors. There is spontaneous symmetry breaking of the local gauge symmetry, and spin or orbital rotational symmetries. 

The Cooper pairing in superfluid 3He is not due to a fermion-phonon interaction but due to spin fluctuations.

The fact that Cooper pairing was possible for different symmetries and mechanisms than for elemental superconductors was significant in that it meant it was reasonable to consider this possibility for superfluidity in neutron stars, and superconductivity in cuprates, strontium ruthenate, heavy fermions, and organic charge transfer salts.

There is rich physics associated with the symmetry breaking: 18 collective modes of the order parameter, textures such as boojums, and exotic vortex cores. For vortices, there is also some (controversial) connection to cosmic strings, including experiments that test the Kibble-Zurek mechanism and the electro-weak phase transition in the early universe.

Aside: My Ph.D. thesis was on the theory of the non-linear interaction of zero sound with the order parameter collective modes in the B-phase.

Leggett's development of the theory of superfluid 3He was amazing and certainly worthy of a Nobel. However, I think he made an even greater contribution to physics through his work on the theory of macroscopic quantum effects in Josephson junctions. This work was the basis for the experimental work that was honoured with the Nobel Prize last year.

With his student Amir Caldeira, Leggett performed concrete calculations of the effects of decoherence on quantum tunnelling in Josephson junctions.

[The NY Times obituary mistakenly says this work began after Leggett moved to Urbana. It was done while he was still at Sussex].

The formalism they developed involving the spectral density is the basis for most theoretical treatments of decoherence in superconducting qubits. A relevant toy model is the spin-boson model, and in 1987 Leggett published a seminal (but rather dense) review on the subject.

Leggett aided our understanding of cuprate superconductors. He contributed to the theoretical ideas that were the basis of the phase-sensitive measurements that established the d-wave nature of the order parameter. He also showed that experiments with inconsistent with  Anderson's interlayer tunneling theory.

I recommend reading Leggett's own scientific autobiography, Matchmaking Between Condensed Matter and Quantum Foundations, and Other Stories: My Six Decades in Physics and his book, The Problems of Physics

2025 Nobel Prize in Physics: Macroscopic quantum effects

John Clarke, Michel H. Devoret, and John M. Martinis received the prize  “for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit.”

The work was published in three papers in PRL in 1984 and 1985. The New York Times has a nice discussion of the award, including comments from Clarke, Martinis, Tony Leggett, and Steve Girvin.

There is some rich, subtle, and beautiful physics here. As a theorist, I comment on the conceptual and theoretical side, but don't want to minimise that doing the experiments was a technical breakthrough.

The experiments were directly stimulated by Tony Leggett, who, beginning in the late 70s, championed the idea that Josephson junctions and SQIDs could be used to test whether quantum mechanics was valid at the macroscopic level. Many in the quantum foundations community were sceptical. Leggett and Amir Caldeira, performed some beautiful, concrete, realistic calculations of the effect of decoherence and dissipation on quantum tunneling in SQUIDs. The results suggested that macroscopic tunneling should be observable.

Aside: Leggett rightly received a Nobel in 2003 for his work on the theory of superfluid 3He. Nevertheless, I believe his work on quantum foundations is even more significant.

Subtle point 1. What do we mean by a macroscopic quantum state?

It is commonly said that superconductors and superfluids are in a macroscopic quantum state. Signatures are the quantisation of magnetic flux in a superconducting cylinder and how the current through a Josephson junction oscillates as a function of the magnetic flux through the junction. I discuss this in the chapter on Quantum Matter in my Very Short Introduction.

Leggett argued that these experiments are explained by the Josephson equations, which treat the phase of the superconducting order parameter as a classical variable. For example, in a SQUID, it satisfies a classical dynamical equation. 

If the state is truly quantum, then the phase variable should be quantised.

Aside: a nice microscopic derivation, starting from BCS theory and using path integrals, of the effective action to describe the quantum dynamics was given in 1982 by Vinay Ambegaokar, Ulrich Eckern, Gerd Schön

Subtle point 2. There are different signatures of quantum theory: energy level quantisation, tunnelling, coherence (interference), and entanglement.

In 1984-5, Clarke, DeVoret, and Martinis observed the first two. Macroscopic quantum coherence is harder to detect and was only observed in 2000. 

In a nice autobiographical article

Matchmaking Between Condensed Matter and Quantum Foundations, and Other Stories: My Six Decades in Physics

Leggett commented in 2020,

Because of the strong prejudice in the quantum foundations community that it would never be possible to demonstrate characteristically quantum-mechanical effects at the macroscopic level, this assertion made us [Leggett and Garg, 1985] the target of repeated critical comments over the next few years. Fortunately, our experimental colleagues were more open-minded, and several groups started working toward a meaningful experiment along the lines we had suggested, resulting in the first demonstrations (29, 30) of MQC [Macroscopic Quantum Coherence] in rf SQUIDs (by then rechristened flux qubits) at the turn of the century. However, it would not be until 2016 that an experiment along the lines we had suggested (actually using a rather simpler protocol than our original one) was carried out (31) and, to my mind, definitively refuted macrorealism at that level.  

I find it rather amusing that nowadays the younger generation of experimentalists in the superconducting qubit area blithely writes papers with words like “artificial atom” in their titles, apparently unconscious of how controversial that claim once was.

Two final comments on the sociology side.

Superconductivity and superfluidity have now been the basis for Nobel Prizes in six years and four years, respectively.

The most widely cited of the three PRLs that were the basis of the Prize is the one on quantum tunnelling with about 500 citations on Google Scholar. (In contrast, Devoret has more than 20 other papers that are more widely cited). From 1986 to 1992 it was cited about a dozen times per year. Between 1993 and 2001 is was only cited a total of 30 times. Since, 2001 is has been cited about 20 times per year.

This is just one more example of how citation rates are a poor measure of the significance of work and a predictor of future success.

Emergence and philosophy

 A challenge in understanding and discussing emergence is that it means different things to different people. This is not surprising given emergence involves diverse and complex phenomena, occurs in a wide range of contexts, and is of interest to people in a diverse range of fields. Recently, I have started to be more precise about how emergence might be defined.

The subject interests philosophers, but it is hard for physicists to glean insights from (and critique) what philosophers say.  I find the following article from 2011 by Bei Lok Hu, helpful.

Emergence: Key physical issues for deeper philosophical inquiries

Hu is not a condensed matter physicist. He is more interested in emergence from its relevance to quantum decoherence and the possibility of space-time being emergent leading to a theory of quantum gravity. Thus, the article is a good entry into literature that I am not familiar with.

Hu gives a nice summary and critique of some of the main philosophical discussions and issues. Here are a few things I have grasped so far. With respect to defining what emergence is Hu writes about three "senses of emergence". The first is below.

Emergence in the sense of difference in manifestations– Role of coarse-graining:

* Different manifestations at different levels of structures, hierarchical in form, and corresponding interactions.

* Requires the identification of the range and precision of measurement, thus interfaces necessarily with an observer’s probing ability and observation range. Effective field theory is of this nature.

* Stability of emergent structures depends on the degree of coarse-graining

* Robustness of emergent structures against the variation of coarse-graining.

(Vaguely in philosopher’s language, the first two bullets correspond to novelty, and the latter two correspond to autonomy.)

I note that this definition of "novelty" is different to mine. I take the plainer definition that at higher levels the system has a property that it does not have at a lower level. A drop of water is wet, but a single molecule is not. A brain is conscious, but a single neuron is not. A lump of solid let is a superconductor, but a few atoms of lead are not. 

This illustrates how the same word can mean different things to physicists and philosophers. Other examples include "reductionism" and "fundamental". 

An important work that engages both physics and philosophy perspectives is "Is More Different? Emergent Properties in Physics," Oxford University DPhil thesis, by Paul Mainwood.

Mainwood summarizes, “... systemic properties are novel, if and only if it is practically impossible to derive them from the microphysical properties mentioned in microphysical supervenience.” ([40] p. 30)

Three proposals of novelty were examined by Mainwood ([40] Sec. 1.5): 

1) a failure of intertheoretic reduction; 

2) an impossibility of deducing the systemic properties from the properties of the parts; or 

3) a failure of mereological supervenience. 

The approaches appeal to three entirely separate distinctions between the properties of parts and wholes; thus according to Mainwood, there are three entirely different sets of criteria for emergence. 

Like me, Hu suggests ontology [reality] should come before epistemology [how we know]. Whereas, philosophers tend to start with epistemology and then try to use that to understand emergence. Understandably, consciousness and the philosophy of mind is a big thing for philosophers. It is often used a starting point for discussions about emergence. However, given consciousness is such a thorny, slippery, and difficult problem, to understand emergence it would be better to start with concrete and tractable examples from physics, such as emergence in condensed matter. 

The final sentence of the acknowledgements in the paper is poignant, amusing, and tragic.

This kind of non mission-driven, non utilitarian work addressing purely intellectual issues is not expected to be supported by any U.S. grant agency.

Many-worlds cannot explain fine tuning

There are several independent lines of argument that are used to support the idea of a multiverse: the many-worlds interpretation of quantum mechanics, the ``landscape problem'' in string theory, and the fine-tuning of fundamental physical constants. Previously, I wrote about four distinct responses to the fine-tuning of the cosmological constant.

I was recently trying to explain the above to a group of non-physicists. One of them [Joanna] had the following objection that I had not heard before. Schrodinger's cat can only exist in one universe within the multiverse. The multiverse involves zillions of universes. However, because of fine-tuning carbon-based life is so improbable that it can only exist in one (or maybe a handful?) of the universes, within the multiverse. Thus, when one observes whether the cat is dead or alive, and the universe ``branches" into two distinct universes, one with a dead cat and the other with a living cat, there is a problem. It is possible that many-worlds interpretation is still correct, but it does not seem possible to claim that many-worlds and the multiverse needed to ``explain'' fine-tuning are the same type of multiverse.

One response might be that Schrodinger's cat is just a silly extrapolation of entanglement to the macroscopic scale. However, the problem remains. Just consider radioactive decay of atoms. Each decay of a single atom should be associated with branching to two distinct universes. Both of those universes are identical, except for whether that single atom has decayed or not. Over history, zillions of radioactive decays have occurred. This means that there are zillions of universes almost identical to the one we live in right now. But, all these zillion universes are fine-tuned to be just like ours.

Is there a problem with this argument?

Addendum. (25 October, 2019).
Fine-tuning got a lot of attention after the 1979 Nature paper, The anthropic principle and the structure of the physical world, by Bernard Carr and Martin Rees.
The end of the article makes explicit the connection with the many-worlds interpretation of quantum theory.

...nature does exhibit remarkable coin- cidences and these do warrant some explanation.... the anthropic explanation is the only candidate and the discovery of every extra anthropic coincidence increases the post hoc evidence for it. The concept would be more palatable if it could be given a more physical foundation. Such a foundation may already exist in the Everett 'many worlds' interpretation of quantum mechanics, according to which, at each observation, the Universe branches into a number of parallel universes, each corresponding to a possible outcome of the observation. The Everett picture is entirely consistent with conventional quantum mechanics; it merely bestows on it a more philosophically satisfying interpretation. There may already be room for the anthropic principle in this picture. 

Wheeler envisages and infinite ensemble of universes all with different coupling constants and so on. Most are 'still-born', in that the prevailing physical laws do not allow anything interesting to happen in them; only those which start off with the right constants can ever become 'aware of themselves'. One would have achieved something if one could show that any cognisable universe had to possess some features in common witti our Universe. Such an ensemble of universes could exist in the same sort of space as the Everett picture invokes. Alternatively, an observer may be required to 'collapse' the wave function. These arguments go a little way towards giving the anthropic principle the status of a physical theory but only a little: it may never aspire to being much more than a philosophical curiosity...

In a review of a book based on a conference about the multiverse, Virginia Trimble states that:

There is also among the authors strong divergence of opinion on whether Hugh Everett's version of many worlds is (just) a quantum multiverse (Tegmark), almost certainly correct and meaningful (Page), or almost certainly wrong or meaningless (Carter). 

Noel Hush (1924- 2019): pioneering theoretical chemist

I was sad to hear last week that Professor Noel Hush died at age 94. Noel [also known as Prof.] was a pioneer in theoretical chemistry and chemical physics. He had a profound influence on both fields, particularly in their development in Australia.

Arguably his greatest scientific contribution was in the theory of electron transfer. Depending on where you are from this is called Hush-Marcus theory, Marcus-Hush theory, or Marcus theory. In particular, in 1958 Hush derived one of the most important equations in chemical physics, which can be used for design principles for functional electronic materials. A key concept here is the notion of diabatic states.

I had the privilege of knowing and working with Prof. Hush on and off over the past decade. As I made an adiabatic transition from condensed matter into chemical physics Prof. Hush provided a lot of encouragement, wisdom, perspective, and ideas. He strongly believed that theoretical chemists and condensed matter theorists could have mutually beneficial interactions. Together with Jeff Reimers and Laura McKemmish, we co-authored seven papers together. The last papers were published when Noel was 90 years old!

Besides his significant legacy of scientific knowledge, there is an incredible legacy of people that he taught, supervised, mentored, encouraged, and collaborated with.

There is an interesting interview of Prof. Hush about his life by Robyn Williams from 2011.

Talk on "crackpot" theories

At UQ there is a great student physics club, PAIN. Today they are having a session on "crackpot" theories in science. Rather than picking on sincere but misguided amateurs I thought I would have a go at "mainstream" scientists who should know better. Here are my slides on quantum biology.

A more detailed and serious talk is a colloquium that I gave six years ago. I regret that the skepticism I expressed then seems to have been justified.

Postscript.
I really enjoyed this session with the students. Several gave interesting and stimulating talks, covering topics such as flat earth, last thursdayism, and The Final Theory of gravity [objects don't fall to the earth but rather the earth rises up to them...]. There were good discussions about falsifiability, Occam's razor, Newton's flaming laser sword, ...
There was an interesting mixture of history, philosophy, humour, and real physics.

I always find to encouraging to encounter students who are so excited about physics that they want to do something like this on a friday night.

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 τhom = 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.

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.

Quantum biology smells bad

I am skeptical of the grand and speculative claims of "quantum biology". 
There is a nice paper in PNAS which systematically considers the specific claim that smell is based on sensing the vibrational frequencies of particular molecules, and rebuts it from both theoretical and experimental points of view.

Implausibility of the vibrational theory of olfaction
Eric Block, Seogjoo Jang, Hiroaki Matsunami, Sivakumar Sekharan, Bérénice Dethier, Mehmed Z. Ertem, Sivaji Gundala, Yi Pan, Shengju Li, Zhen Li, Stephene N. Lodge, Mehmet Ozbil, Huihong Jiang, Sonia F. Penalba, Victor S. Batista, and Hanyi Zhuang.

I thank Suggy Jang for bringing the paper to my attention.

Quantum nuclear effects in condensed phase chemistry

I am currently in Telluride for a meeting on Quantum effects in condensed phase systems. Two years ago I attended a similar meeting and in preparing it has been helpful to re-read several posts I wrote stimulated by that meeting.

In my first post, I listed possible quantum effects [zero-point motion, tunnelling, geometric phases, entanglement, ...] and pointed how generally one expects a condensed phase environment [protein, glass, solvent] for a molecular system will tend to reduce these quantum effects by decoherence.

I then asked two big questions.
Are there any instances where the environment can
A. enhance quantum effects?
B. lead to qualitatively new effects (e.g. associated with collective degrees of freedom) that are absent in the gas phase?

I clarified what I meant by a trivial vs. non-trivial enhancement of a quantum effect, from a physics point of view. An example of a "trivial" enhancement is where the environment changes the molecular geometry to enhance the effect. But I stressed that such an enhancement may be highly valuable from a chemistry or biochemistry point of view.

In a comment, Gautam Menon suggested that the Surface Enhanced Raman scattering was a nice example of a non-trivial enhancement. It is certainly spectacular, with enhancements as large as 10^11. However, I am not sure this is the type of quantum effect I am thinking of. The actual mechanism of the effect is still debated [see this paper] and I am not qualified to consider the relative merits of the alternative explanations, but it does look to me like it could be viewed as a semi-classical effect.

Tom Miller suggested to me that the solvation of single electrons and the associated polarons may be a suitable example of B.

I suggested that there were two important organising principles for describing and understanding quantum nuclear effects
1. Competing quantum effects
2. Rate processes can be dominated by rare quantum events.

I am looking forward to the meeting.

What are the ten key concepts in quantum many-body physics?

Here I consider quantum many-body theory, as it spans from quantum field theory to nuclear physics to ultra cold atomic gases to solid state physics to quantum chemistry.

Here is my tentative list of the ten most important key concepts.
n.b. I am not concerned with key techniques (e.g. path integrals, renormalisation group, Green's functions, Feynman diagrams, imaginary time (KMS), numerical methods....). That is a separate topic. Unfortunately, in most many-body theory texts the concepts are lost in the midst of all the technical details. Furthermore, concepts are what experimentalists need to know and understand.

1. Emergence
This is the overarching concept that underscores almost all the others. Reality is stratified and at each length, energy, and time scale distinctly new phenomena, interactions and entities can emerge. More is different.

2. Effective Hamiltonians
At each strata there is some Hamiltonian that describes the "particles" and interactions between them. The parameters in this Hamiltonian can sometimes be determined from experiment.

3. Quasi-particles
There are two cases. In the simplest case, due to adiabatic continuity, the quasi-particles have the same quantum numbers and statistics as the constituent particles (e.g., Fermi liquid theory). But, their mass and spin-g factors can be significantly different from the free particles. The second and more exciting case is where the quasi-particles have different quantum numbers and/or statistics to
the constituent particles (e.g. Fractional Quantum Hall effect, spinons, and Luttinger liquid).

4. Renormalisation
This explains how the effective interactions at one strata are related to those at a lower strata (or equivalently how high energy virtual processes lead to low energy real interactions). Examples range from weak interactions in a Fermi liquid to asymptotic freedom in QCD to the van der Waals attraction between two neutral atoms.

5. Incoherent excitations
Sum rules provide a means to understand the redistribution of spectral weight. Quasi-particles don't exhaust the total spectral weight.
This also connects to Hubbard bands, bad metals, quantum decoherence, and the condensate fraction for superfluids and superconductors.

6. Spontaneously Broken Symmetry
This leads to new states of matter and new collective excitations, including Goldstone bosons (e.g. phonons and magnons) and massive particles such as the Higgs boson. This is also connected to rigidity, but that does have a classical analogue too.

7. Emergent energy scales
These can be orders of magnitude different (always smaller?) from the energy scales in the underlying Hamiltonian. Often they reflect non-perturbative effects, as in the BCS energy gap or the Kondo temperature.

8. Emergent length scales

9. The fluctuation-dissipation theorem
This means we can calculate linear transport (i.e. non-equilibrium) properties from fluctuations in thermal equilibrium. Inelastic scattering experiments can then be related to dynamical correlations.

10. Topology sometimes matters
Examples include topological excitations (e.g. vortices), topological terms in the action (e.g. for quantum spin chains and the Haldane conjecture), topological insulators, and topological order in the Quantum Hall effect. Topology is also somehow involved in anomaly cancellation.

Piers Coleman's article (focussing on condensed matter) provides a nice discussion of some of these concepts.

What do you think? What should I add or subtract from this list?

Some might suggest entanglement and/or quantum criticality or there own current favourite hot topic. However, I still remain to be convinced that these are key organising principles that are essential for understanding broad ranges of systems, rather than currently fashionable exotica.

I might include the Mott insulator, but I am not clear how that is relevant beyond solid state physics.

Is the list helpful? I am considering spending more time on this: perhaps a blog post on each concept, then a colloquium style talk, and a short tutorial review article.
I think the only mathematical entity needed to understand and illustrate all of this is a spectral function.
Any feedback would be appreciated.

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.

A brilliant insight about quantum decoherence in electronic circuits

Yesterday, Matthew Woolley gave an interesting Quantum science seminar at UQ about some of his recent work on Photon assisted tunnelling with non-classical light.

I just want to focus on one point that was deeply imbedded in the talk. It is a idea that is profound and central to the physics of quantum electronic circuits. The idea is so old now its profoundness and brilliance may be lost on a new generation.
The idea and result is easiest for me to explain in terms of the figure below which describes a superconducting (Josephson junction) qubit connected to an electrical circuit. It is taken from this review.

One can quantise the electromagnetic field and consider a spin-boson model to describe decoherence and dissipation of the qubit. This is associated with a spectral density that is proportional to frequency with a dimensionless pre factor alpha, which for this circuit is given by

where R_V is the electrical resistance of the circuit, R_K is the quantum of resistance, and the C's are capacitances.
Similar physics is at play in normal tunnel junctions (see for example this important paper, highlighted by Matthew in his talk).

Why do I find this profound?
First, this is a very simple formula that depends only on macroscopic parameters of the electrical circuit. One does not have to know anything about the microscopic details of  all the different electronic degrees of freedom in the circuit or how they individually couple to the qubit. I find this surprising.
Second, the underlying physics is the fluctuation-dissipation theorem. The quantum noise in the electronic circuit is related to fluctuations in the current. By Kubo and the fluctuation-dissipation relation tell us the fluctuations in the current are essentially the conductivity [the inverse of the resistivity].

Who was the first to have this insight and calculate this?
I feel it was Caldeira and Leggett, but I can't find the actual equation with the circuit resistance in their 1983 paper.
Or did someone else do this earlier?

Because of the above, whenever the spectral density depends linearly on the frequency, Leggett (and now everyone) calls it ohmic dissipation.

I first learnt this through the thesis work of my student Joel Gilmore, and described in this review. There we considered a more chemical problem, two excited electronic states of a molecule that are in a polar dielectric solvent. The coupling to the environment is completely specified in terms of the frequency dependent dielectric constant of the solvent (and some geometric factors).

Update: Caldeira answers the question in a comment below.

Condensed phase dynamics in Telluride

Last night I was stranded at Denver airport en route to the bi-annual Condensed phase dynamics meeting at the Telluride Science Research Center.  This is the third time I have been to this wonderful meeting. Getting there can be a real hassle. But, then you look at the scenery and enjoy the science and it seems worth it.

Unfortunately, due to the travel delays I missed the first two talks, by Joe Subotnik and Nandini Ananth.

Dominika Zgid gave a chemist's perspective on "How to make dynamical mean theory quantitative". Some of her work was discussed in a my last post. Today she mostly discussed a generalisation of iterative perturbation theory as an "impurity solver" for DMFT problems with multiple orbitals. See this preprint.

Peter Rossky discussed quantum chemical simulations of exciton dynamics in conjugated polymers.

This was motivated by an experiment reported in Science that claimed evidence for quantum coherent transport of excitons along a polymer chain at room temperature. Several oscillations were seen in the fluorescence polarisation anisotropy  as it decays in about a picosecond. These oscillations were identified with quantum inference [Rabi oscillations] between different exciton states delocalised over the polymer chain.

It turns out the experimental results have a much more mundane explanation.
The simulations of Adam Willard and Rossky are of classical dynamics on the adiabatic excited state potential energy surface calculated from a parameterised PPP [Pariser-Parr-Pople] model [basically a Hubbard model with long-range Coulomb interactions. They see oscillations similar to those in the experiment and can identified simply with classical nuclear motion associated with the polymer backbone stretching [phonons] in response to photo-excitation.

Much-hyped experiments claiming to show quantum coherence in photosynthetic complexes, probably also have a similar classical explanation in terms of nuclear dynamics rather than electronic coherences. A concrete interpretation in terms of vibrational coherences is in this PNAS paper. My skepticism of these "quantum biology" experiments has been expressed in many earlier posts.

Hopefully, tomorrow I will blog about talks from Eran Rabani, Todd Martinez, and Dvira Segal.

The problem with D-wave's "quantum" computer

Someone from the company D-wave is coming to UQ [not the physics department] next week to give a seminar. Their claim of producing the first commercial quantum computer has met with considerable skepticism. This has been led by Scott Aaronson, on his blog. It contains some nice detailed and thoughtful discussion of the relevant scientific issues.

But here is the key concern, that I fully agree with,

As I’ve said many times, I’d support even the experiments that D-Wave was doing, if D-Wave and its supporters would only call them for what they were: experiments.  Forays into the unknown.  Attempts to find out what happens when a particular speculative approach is thrown at NP-hard optimization problems.  It’s only when people obfuscate the results of those experiments, in order to claim something as “commercially useful” that quite obviously isn’t yet, that they leave the realm of science, and indeed walk straight into the eager jaws of skeptics ...

I think this reflects larger problems in society, once the [money] tail wags the donkey problems occur.

At the end of the day, there is no real evidence that
-there is any large scale quantum entanglement in the D-wave devices [there is some indirect evidence [i.e. not violation of Bell inequalities] of small scale entanglement.
-they have achieved any real speedup over what a classical computer can do [see this preprint].

Concerted vs sequential processes in chemistry

A basic but important and interesting question in physical chemistry concerns a chemical reaction or process that involves two steps: A to B to C.
Do they occur sequentially or can they occur simultaneously, i.e., in a concerted or co-operative manner?
Two examples of particular interest are coupled electron-proton transfer and double proton transfer.
The figure below shows a carboxylic acid dimer involving two hydrogen bonds

The configuration above has the same energy as the tautomer with the top H moved to the right and the bottom H moved to the left. But, does this reaction occur by simultaneously moving the protons or first moving one and then the second.

For the case of double proton transfer in dimers of a model of a DNA base pair [shown in the picture below] there has been some controversy about whether the process is concerted or sequential. This brief letter by Kwon and Zewail in PNAS gives the relevant references. They stress that some of the controversy seems to stem from confusion about clearly defining what one means by the two options. They argue the weight of the evidence is for sequential.

Another example concerns the role of intermediate electronic states in charge separation processes in molecular photovoltaic materials.

I am interested in exploring simple effective Hamiltonians that might be used to come up with some general criteria and experimental signatures for discriminating between concerted and sequential processes.

Skepticism should be the default reaction to exotic claims

A good principle in science is "extra-ordinary claims require extra-ordinary evidence", i.e. the more exotic and unexpected the claimed new phenomena the greater the evidence needs to be before it should be taken seriously. A classic case is the recent CERN experiment claiming to show that neutrinos could travel faster than the speed of light. Surely it wasn't too surprising when it was found that the problem was one of detector calibration. Nevertheless, that did not stop many theorists from writing papers on the subject. Another case, are claims of "quantum biology".

About a decade ago some people tried to get me interested in some anomalous experimental results concerning elastic scattering of neutrons off condensed phases of matter. They claimed to have evidence for quantum entanglement between protons on different molecules for very short time scales and [in later papers] to detect the effects of decoherence on this entanglement. An example is this PRL which has more than 100 citations, including exotic theory papers stimulated by the "observation."

Many reasons led me not to get involved: mundane debates about detector calibration, a strange conversation with one of the protagonists, and discussing with Roger Cowley his view that the theoretical interpretation of the experiments was flawed, and of course, "extra-ordinary claims require extra-ordinary evidence"....

Some of the main protagonists have not given up. But the paper below is a devastating critique of their most recent exotic claims.

Spurious indications of energetic consequences of decoherence at short times for scattering from open quantum systems by J. Mayers and G. Reiter

Mayers is the designer and builder of the relevant spectrometer. Reiter is a major user. Together they have performed many nice experiments imaging proton probability distributions in hydrogen bonded systems.
They argue that the unexpected few per cent deviations from conventional theory that are "evidence" just arise from incorrect calibration of the instrument.