Thermal equilibrium in Gaussian dynamical semigroups

TL;DR

This paper characterizes Gaussian dynamical semigroups in quantum systems that have thermal equilibrium states, establishing explicit relations between their parameters and the thermal state, and analyzing detailed-balance conditions.

Contribution

It provides a complete characterization of Gaussian dynamical semigroups with thermal equilibrium, linking their parameters to the thermal state and detailed-balance conditions.

Findings

Explicit relation between diffusion/dissipation matrices and thermal covariance

Identification of semigroups sharing the same thermal state

Analysis of temperature dependence via detailed-balance condition

Abstract

We characterize all Gaussian dynamical semigroups in continuous variables quantum systems of n-bosonic modes which have a thermal Gibbs state as a stationary solution. This is performed through an explicit relation between the diffusion and dissipation matrices, which characterize the semigroup dynamic, and the covariance matrix of the thermal equilibrium state. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices, and the identification of different Gaussian dynamical semigroups which shares the same thermal equilibrium state.