Asymptotic Dynamics of Open Quantum Systems and Modular Theory

TL;DR

This paper investigates the long-term behavior of finite-dimensional open quantum systems, linking their asymptotic dynamics to modular theory, and providing conditions for unitarity of the peripheral map.

Contribution

It introduces a structure theorem for the peripheral map, characterizes conditions for its unitarity, and connects asymptotic dynamics with modular theory.

Findings

Conditions for the unitarity of the peripheral map

Presence of permutations affects asymptotic map structure

Connection established between asymptotic map and modular theory

Abstract

In this Article, several aspects of the asymptotic dynamics of finite-dimensional open quantum systems are explored. First, after recalling a structure theorem for the peripheral map, we discuss sufficient conditions and a characterization for its unitarity. Interestingly, this is not always guaranteed due to the presence of permutations in the structure of the asymptotic map. Then, we show the connection between the asymptotic map and the modular theory by Tomita and Takesaki.