Thursday, August 22, 2013

Defining non-trivial quantum effects in chemical dynamics

Bill Miller has a very nice Perspective: Quantum or Classical coherence? in the Journal of Chemical Physics. I thank him for explaining some of it to me today.

He clearly defines what he considers to be a truly quantum effect in chemical dynamics.
It is particularly interesting because by his definition Rabi oscillations are not quantum. They are just like two coupled classical harmonic oscillators.

He starts with a Feynman path integral representation of some time-dependent correlation function and considers the semi-classical (SC) limit. The correlation function can be written as an initial value representation (IVR). If one linearises the paths (LSC) one obtains classical Wigner functions and one cannot capture quantum interference effects [e.g. double slit interference which involves paths with more than infinitesimal separation].

Tao and Miller considered the semi-classical path-integral representation of the spin-boson model. They use the Meyer-Miller-Stock-Thoss representation to map the "spin" [two-level system] to a pair of harmonic oscillators [for condensed matter physicists these are Schwinger bosons]. This allows a semi-classical treatment of the two-level system. Then the Rabi oscillations are just like transfer of energy backwards and forwards between two coupled classical harmonic oscillators. This leads to the figure below.
The "Present model" refers to the LSC-IVR treatment, i..e there is no quantum interference.

Ishizaki-Fleming refers to a much more sophisticated "quantum" treatment working towards describing the much-hyped [and probably mistaken] "quantum coherence" of exciton transfer in photosynthetic systems.

The article also contains several other concrete examples: some with and some without quantum coherence. A Tully non-adiabatic problem is particularly interesting because the nuclei exhibit quantum coherence but the electrons don't.

1 comment:

  1. Many thanks for bringing this to my attention.

    The point at the end is very astute. What is quantum and what is classical depends on the information one wants out of the system (i.e. the observables of interest).

    What is not immediately clear is whether the linearized SC-IVR could describe the "quantum" effects as classical ones if the mapping was performed with a different set of observable operators. I think the answer has to be 'yes'.