Relaxation of a Simple Quantum Random Matrix Model

TL;DR

This paper derives the relaxation dynamics of a quantum particle on two sites with random matrix interactions, providing effective equations in the weak coupling limit applicable to various similar models.

Contribution

It introduces a method to derive effective relaxation equations for a quantum system modeled by random matrices in the weak coupling regime.

Findings

Derived effective relaxation equations for the quantum model.

Applicable to a range of models with similar structure.

Provides insights into quantum relaxation behavior.

Abstract

We will derive here the relaxation behavior of a simple quantum random matrix model. The aim is to derive the effective equations which rise when a random matrix interaction is taken in the weak coupling limit. The physical situation this model represents is that a quantum particle restricted to move on two sites, where every site has N possible energy states. The hopping from one site to another is then modeled by a random matrix. The techniques used here can be applied to many variations of the model.