Bubble nucleation and quantum initial conditions in classical statistical simulations

TL;DR

This paper examines the validity of classical-statistical lattice simulations initialized with quantum-like fluctuations for modeling quantum bubble nucleation, finding that previous numerical agreements are coincidental and not reliable.

Contribution

It critically assesses the use of quantum-like initial conditions in classical simulations and demonstrates the limitations as dimensions increase.

Findings

Quantum-like initial conditions produce coincidental agreement in 1+1 dimensions.

The agreement depends on parameters and lattice cut-offs.

The agreement vanishes when moving from 1+1 to 2+1 dimensions.

Abstract

Classical-statistical lattice simulations provide a useful approximation to out-of-equilibrium quantum field theory, but only for systems exhibiting large occupation numbers, and only for phenomena that are not intrinsically quantum mechanical in nature. In certain special circumstances, it can be appropriate to initialize such real-time simulations with quantum-like zero-point fluctuations. We will revisit these points, and investigate reports that quantum bubble nucleation rates in 1+1 dimensions can be computed through the classical evolution of such a quantum-like initial condition. We find that although intriguing, the reported numerical agreement between classical-statistical simulations and the quantum nucleation rate in 1+1 dimensions is a coincidence, which is not specific to this choice of initialisation, is parameter and lattice cut-off dependent and disappears as the number of space-dimensions increases from 1+1 to 2+1