# Noncommutative phase-space effects in thermal diffusion of Gaussian states

## TL;DR

This paper investigates how noncommutative phase-space influences the thermal diffusion and time evolution of Gaussian states in a thermal environment, revealing effects on fidelity and non-Markovianity.

## Contribution

It introduces a method to detect noncommutative effects via fidelity analysis during thermal diffusion of Gaussian states.

## Key findings

- Fidelity differences signal noncommutative effects.
- Monotonicity of fidelity relates to non-Markovian behavior.
- Noncommutative effects impact the thermalization process.

## Abstract

Noncommutative phase-space and its effects have been studied in different settings in physics, in order to unveil a better understanding of phase-space structures. Here, we use the thermal diffusion approach to study how noncommutative effects can influence the time evolution of a one-mode Gaussian state when in contact with a thermal environment obeying the Markov approximation. Employing the cooling process and considering the system of interest as a one-mode Gaussian state, we show that the fidelity comparing the Gaussian state of the system in different times and the asymptotic thermal state is useful to sign noncommuative effects. Besides, by using the monotonicity behavior of the fidelity, we discuss some aspects of non-Markovianity during the dynamics.