Quantum master equation for a system influencing its environment

TL;DR

This paper derives a more general quantum master equation that accounts for energy exchange and conservation in a system-environment setup, improving the description of relaxation in nanoscopic quantum systems.

Contribution

It introduces a perturbative, non-Markovian quantum master equation that includes energy exchange effects and reduces to the Redfield equation under certain conditions.

Findings

The new master equation accurately describes relaxation in isolated nanoscopic systems.

Comparison with exact solutions shows the importance of energy exchange in modeling.

The Markovian approximation captures long-time relaxation behavior.

Abstract

A perturbative quantum master equation is derived for a system interacting with its environment, which is more general than the ones derived before. Our master equation takes into account the effect of the energy exchanges between the system and the environment and the conservation of energy in a finite total system. This master quantum describes relaxation mechanisms in isolated nanoscopic quantum systems. In its most general form, this equation is non-Markovian and a Markovian version of it rules the long-time relaxation. We show that our equation reduces to the Redfield equation in the limit where the energy of the system does not affect the density of state of its environment. This master equation and the Redfield one are applied to a spin-environment model defined in terms of random matrices and compared with the solutions of the exact von Neumann equation. The comparison proves the necessity to allow energy exchange between the subsystem and the environment in order to correctly describe the relaxation in isolated nanoscopic total system.