Finite Temperature Simulations from Quantum Field Dynamics?

TL;DR

This paper introduces a Hartree ensemble method for simulating quantum field dynamics in 1+1 dimensions, demonstrating quantum thermalization and its transition to classical equipartition, with improved computational efficiency.

Contribution

The paper presents a novel Hartree ensemble approach to approximate quantum field dynamics, effectively capturing quantum thermalization and enhancing numerical performance.

Findings

Quantum particles initially thermalize with Bose-Einstein distribution.

Distribution shifts towards classical equipartition over time.

Quantum thermalization occurs faster than equipartition with proper initial conditions.

Abstract

We describe a Hartree ensemble method to approximately solve the Heisenberg equations for the \phi^4 model in 1+1 dimensions. We compute the energies and number densities of the quantum particles described by the \phi field and find that the particles initially thermalize with a Bose-Einstein distribution for the particle density. Gradually, however, the distribution changes towards classical equipartition. Using suitable initial conditions quantum thermalization is achieved much faster than the onset of this undesirable equipartition. We also show how the numerical efficiency of our method can be significantly improved.