Additive and multiplicative noise driven systems in1+1dimensions: Waiting time extraction of nucleation rates

Abstract

We study the rate of true vacuum bubble nucleation numerically for a ${\ensuremath{\varphi}}^{4}$ 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 3 or more slower for the multiplicative compared to the additive model with the same dimensionless parameter choices. Both cases lead to high confidence level linear fits of $\mathrm{ln}\ensuremath{\tau}\mathrm{vs}{T}^{\ensuremath{-}1}$ plots, in agreement with semiclassical nucleation rate predictions.