Simulating nonequilibrium quantum fields with stochastic quantization techniques

TL;DR

This paper introduces a novel lattice simulation method for nonequilibrium quantum fields in Minkowski space-time using stochastic quantization, enabling direct real-time quantum dynamics analysis in 3+1 dimensions.

Contribution

It develops a stochastic quantization approach with an additional Langevin-time to simulate nonequilibrium quantum fields directly in Minkowski space.

Findings

Successfully resolves unstable Langevin dynamics.

Demonstrates comparison between quantum and classical field results.

Provides a new tool for studying heavy-ion collision phenomena.

Abstract

We present lattice simulations of nonequilibrium quantum fields in Minkowskian space-time. Starting from a non-thermal initial state, the real-time quantum ensemble in 3+1 dimensions is constructed by a stochastic process in an additional (5th) ``Langevin-time''. For the example of a self-interacting scalar field we show how to resolve apparent unstable Langevin dynamics, and compare our quantum results with those obtained in classical field theory. Such a direct simulation method is crucial for our understanding of collision experiments of heavy nuclei or other nonequilibrium phenomena in strongly coupled quantum many-body systems.