Dependence of Repeated Interaction Asymptotic States on Environment

TL;DR

This paper extends the understanding of how the asymptotic states of a quantum system depend on the environment's initial states, including pure states, by modifying the effective dynamics generator.

Contribution

It generalizes previous results to a broader class of initial environment states, including pure states, through a simple modification of the effective dynamics generator.

Findings

Asymptotic states depend on initial environment states.

The analysis applies to pure initial states of environment probes.

A modified generator captures the dependence on initial states.

Abstract

Consider a quantum system $\cS$ that interacts sequentially with a chain (environment) of identical probes ${\cal C} = \cP+\cP+...$, with each interaction governed by a fixed interaction time $\tau$ and operator $V$. It is known how to construct the asymptotic state (large times) if the initial states of $\cP$ belong to a class of so-called reference states. We generalize the analysis to a broader class of initial states, including the physically important situation of pure states. This is done by a simple modification to the effective dynamics generator.