Spin relaxation in a complex environment

TL;DR

This paper investigates how a two-level quantum system interacts with a complex environment modeled by Gaussian orthogonal random matrices, revealing conditions for thermalization and the emergence of a master equation in strong coupling regimes.

Contribution

It introduces a model of a two-level system coupled to a complex environment using GORM and analyzes the spectral and dynamical effects, including a critical interaction strength for self-averaging behavior.

Findings

Existence of a critical interaction value depending on environment level spacing.

In the strong coupling regime, the dynamics obey a master equation.

The two-level system thermalizes under certain conditions.

Abstract

We report the study of a model of a two-level system interacting in a non-diagonal way with a complex environment described by Gaussian orthogonal random matrices (GORM). The effect of the interaction on the total spectrum and its consequences on the dynamics of the two-level system are analyzed. We show the existence of a critical value of the interaction, depending on the mean level spacing of the environment, above which the dynamics is self-averaging and closely obey a master equation for the time evolution of the observables of the two-level system. Analytic results are also obtained in the strong coupling regimes. We finally study the equilibrium values of the two-level system population and show under which condition it thermalizes to the environment temperature.