Additive and Multiplicative Noise Driven Systems in 1+1 Dimensions: Waiting Time Extraction of Nucleation Rates

TL;DR

This study numerically investigates bubble nucleation rates in a 1+1 dimensional phi^4 field system with thermal noise, comparing additive and multiplicative noise effects and introducing a new method for extracting nucleation times.

Contribution

It introduces a novel approach using the full distribution of nucleation times and compares additive and multiplicative noise effects in a 1+1D model.

Findings

Nucleation time distributions fit a gamma distribution.

Nucleation rates are significantly slower in multiplicative noise models.

Linear ln(nucleation time) vs. 1/T plots agree with semiclassical predictions.

Abstract

We study the rate of true vacuum bubble nucleation numerically for a phi^4 field system coupled to a source of thermal noise. We compare in detail the cases of additive and multiplicative noise. We pay special attention to the choice of initial field configuration, showing the advantages of a version of the quenching technique. We advocate a new method of extracting the nucleation time scale that employs the full distribution of nucleation times. Large data samples are needed to study the initial state configuration choice and to extract nucleation times to good precision. The 1+1 dimensional models afford large statistics samples in reasonable running times. We find that for both additive and multiplicative models, nucleation time distributions are well fit by a waiting time, or gamma, distribution for all parameters studied. The nucleation rates are a factor three or more slower for the multiplicative compared to the additive models with the same dimensionless parameter choices. Both cases lead to high confidence level linear fits of ln(nucleation time) vs. 1/T plots, in agreement with semiclassical nucleation rate predictions.