# Geometry of quantum evolution in a nonequilibrium environment

## TL;DR

This paper investigates how a nonequilibrium environment influences the geometric phase and evolution path of quantum systems, revealing environmental effects on quantum coherence and non-Markovian behavior.

## Contribution

It derives a new expression for the geometric phase considering nonequilibrium environmental effects on quantum evolution.

## Key findings

- Frequency shift due to environment affects geometric phase
- Nonequilibrium environment lengthens evolution path
- Reduces dynamical decoherence and non-Markovian effects

## Abstract

We theoretically study the geometric effect of quantum dynamical evolution in the presence of a nonequilibrium noisy environment. We derive the expression of the time dependent geometric phase in terms of the dynamical evolution and the overlap between the time evolved state and initial state. It is shown that the frequency shift induced by the environmental nonequilibrium feature plays a crucial role in the geometric phase and evolution path of the quantum dynamics. The nonequilibrium feature of the environment makes the length of evolution path becomes longer and reduces the dynamical decoherence and non-Markovian behavior in the quantum dynamics.