Proposal of a computational approach for simulating thermal bosonic fields in phase space

TL;DR

This paper introduces a novel computational method for simulating thermal bosonic fields in phase space by augmenting the Wigner representation with Nosé-Hoover thermostats, enabling numerical studies of non-equilibrium thermal quantum fields.

Contribution

It proposes a new approach combining Wigner phase space methods with Nosé-Hoover thermostats to simulate thermal quantum fields, bridging thermo field dynamics and phase space techniques.

Findings

Demonstrates how to implement Nosé-Hoover thermostats in Wigner phase space

Shows numerical simulation of non-equilibrium thermal field distributions

Provides a computational framework for thermal bosonic field analysis

Abstract

When a quantum field is in contact with a thermal bath, the vacuum state of the field may be generalized to a thermal vacuum state, which takes into account the thermal noise. In thermo field dynamics, this is realized by doubling the dimensionality of the Fock space of the system. Interestingly, the representation of thermal noise by means of an augmented space is also found in a distinctly different approach based on the Wigner transform of both the field operators and density matrix, which we pursue here. Specifically, the thermal noise is introduced by augmenting the classical-like Wigner phase space by means of Nos\'e-Hoover chain thermostats, which can be readily simulated on a computer. In this paper, we illustrate how this may be achieved and discuss how non-equilibrium quantum thermal distributions of the field modes can be numerically simulated.