Dynamics of Quantum-Classical Systems in Nonequilibrium Environments

TL;DR

This paper develops exact equations for the nonequilibrium dynamics of quantum-classical systems, enabling analysis of their average behaviors and correlations without solving the full density operator, with applications to reaction-diffusion processes.

Contribution

It introduces a novel approach to derive exact equations of motion for quantum-classical systems out of equilibrium, bypassing the need for density operator evolution.

Findings

Derived reaction-diffusion equations coupled to fluid dynamics.

Analyzed nonequilibrium steady states and reaction rates.

Provided correlation functions for dissipative coefficients.

Abstract

The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than evaluating the evolution of the mixed quantum-classical density operator, we derive exact equations of motion for the nonequilibrium average values of a set of operators or variables, along with correlation function expressions for the dissipative coefficients that enter these equations. These equations are obtained by requiring that the exact nonequilibrium averages are equal to local nonequilibrium averages that depend on auxiliary fields whose values satisfy evolution equations obtained using projection operator methods. The results are illustrated by deriving reaction-diffusion equations coupled to fluid hydrodynamic equations for a dilute solution of quantum particles that can exist in two metastable states. Nonequilibrium steady states are discussed along with the reaction rate and diffusion correlation functions that characterize such states.