Approach to Equilibrium of a Nondegenerate Quantum System: Decay of Oscillations and Detailed Balance as Separate Effects of a Reservoir

TL;DR

This paper develops a unified master equation theory to separately analyze how a nondegenerate quantum system approaches equilibrium through oscillation damping and detailed balance, with applications in molecular energy transfer.

Contribution

It introduces a transparent formalism that distinguishes and addresses the effects of phase randomization and phase space considerations in quantum system equilibration.

Findings

The theory successfully models decay of oscillations in quantum systems.

It explains the separate roles of phase randomization and phase space in reaching equilibrium.

Applications include energy transfer in molecular aggregates and photosynthetic centers.

Abstract

The approach to equilibrium of a nondegenerate quantum system involves the damping of microscopic population oscillations, and, additionally, the bringing about of detailed balance, i.e. the achievement of the correct Boltzmann factors relating the populations. These two are separate effects of interaction with a reservoir. One stems from the randomization of phases and the other from phase space considerations. Even the meaning of the word `phase' differs drastically in the two instances in which it appears in the previous statement. In the first case it normally refers to quantum phases whereas in the second it describes the multiplicity of reservoir states that corresponds to each system state. The generalized master equation theory for the time evolution of such systems is here developed in a transparent manner and both effects of reservoir interactions are addressed in a unified fashion. The formalism is illustrated in simple cases including in the standard spin-boson situation wherein a quantum dimer is in interaction with a bath consisting of harmonic oscillators. The theory has been constructed for application in energy transfer in molecular aggregates and in photosynthetic reaction centers.