On a Random Matrix Models of Quantum Relaxation

TL;DR

This paper rigorously proves properties of a random matrix model describing quantum relaxation in a two-level system interacting with a large reservoir, extending previous results with new insights.

Contribution

It provides detailed proofs of earlier results and introduces a new finding about the behavior of the quantum relaxation model.

Findings

Derived formulas for the reduced density matrix as reservoir size tends to infinity

Established properties and asymptotic regimes of the model

Presented a new fact about the model's behavior

Abstract

Earlier two of us (J.L. and L.P.) considered a matrix model for a two-level system interacting with a $n\times n$ reservoir and assuming that the interaction is modelled by a random matrix. We presented there a formula for the reduced density matrix in the limit $n\to \infty $ as well as several its properties and asymptotic forms in various regimes. In this paper we give the proofs of the assertions, and present also a new fact about the model.