An ETH-ansatz-motivated environmental-branch approach to open quantum systems

TL;DR

This paper introduces a new method for deriving master equations for a small quantum system coupled to a chaotic environment, utilizing the ETH ansatz and environmental branch overlaps to predict decoherence.

Contribution

The paper develops a generic approach based on environmental branches and ETH to derive master equations, justifying the Born approximation and demonstrating Markovian behavior.

Findings

Predicts decoherence rates consistent with random-matrix theory.

Provides a framework to justify the Born approximation.

Shows Markovian evolution of the reduced density matrix.

Abstract

In this paper, a method is developed for the study of a generic small central quantum system, which is locally coupled to an environment as a many-body quantum chaotic system that satisfies the eigenstate thermalization hypothesis (ETH) ansatz. The approach is based on properties of environmental branches of the total system's state, the overlaps of which give the reduced density matrix (RDM) of the central system. To study evolution of the RDM within a finite time period, the period is divided into a series of short intervals, within each of which the RDM is computed by making use of a formal solution to the time evolution of the environmental branches. The expressions thus obtained are simplified by the ETH ansatz and, further, by decay of phase correlations among the environmental branches, the latter of which also originates from chaotic dynamics of the environment. This gives a generic method of deriving master equation. And, as an application, a master equation is derived in a simplest nontrivial case, which predicts a decoherence rate in agreement with that predicted by the random-matrix theory. Furthermore, the Born approximation, which is employed in the ordinary approach to master equation, can be justified within the proposed framework; and a Markovian feature is shown for the RDM's evolution in an effective sense.