Quantum phase space function formulation of reactive flux theory

TL;DR

This paper develops a quantum reactive flux theory using phase space distribution functions, deriving a quantum transmission coefficient that accounts for quantum effects and temperature dependence, extending classical formulations to quantum regimes.

Contribution

It introduces a quantum phase space formulation of reactive flux theory, deriving a quantum transmission coefficient applicable to arbitrary noise correlation and temperature, including non-Markovian effects.

Findings

Quantum transmission coefficient depends on temperature, especially at low temperatures.

The theory applies to both Markovian and non-Markovian noise.

Quantum effects significantly influence reaction rates at low temperatures.

Abstract

On the basis of a coherent state representation of quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee {\it et al}, Phys. Rev. E {\bf65}, 021109 (2002); {\bf66}, 051105 (2002)]. We extend this approach to formulate reactive flux theory in terms of quantum phase space distribution functions and to derive a time dependent quantum transmission coefficient - a quantum analogue of classical Kramers'-Grote-Hynes coefficient in the spirit of Kohen and Tannor's classical formulation. The theory is valid for arbitrary noise correlation and temperature. The specific forms of this coefficient in the Markovian as well as in the non-Markovian limits have been worked out in detail for intermediate to strong damping regime with an analysis of quantum effects. While the classical transmission coefficient is independent of temperature, its quantum counterpart has significant temperature dependence particularly in the low temperature regime.