The Gaussian entropy of fermionic systems

TL;DR

This paper investigates the entropy and decoherence of fermionic quantum systems using a Gaussian approximation, analyzing how interactions and temperature influence system behavior and thermalization.

Contribution

It introduces a Gaussian Ansatz for fermionic density operators to study entropy and decoherence, including applications to relativistic quantum fields with mass mixing.

Findings

Fermionic systems decohere effectively under strong coupling and high temperature.

The system approaches environmental temperature during decoherence.

Gaussian approximation captures key features of fermionic entropy and thermalization.

Abstract

We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of these correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields.