Dynamics of defect formation
Esteban Moro, Grant Lythe
TL;DR
This paper analyzes defect formation during a dynamic symmetry-breaking transition with noise and inertia, providing exact solutions and numerical validation across different damping regimes.
Contribution
It introduces an exact analytical approach to predict defect numbers in dynamic transitions considering noise and inertia effects.
Findings
Exact calculation of defect density as a function of transition rate.
Validation of the analytical model with numerical simulations.
Identification of underdamped dynamics signatures.
Abstract
A dynamic symmetry-breaking transition with noise and inertia is analyzed. Exact solution of the linearized equation that describes the critical region allows precise calculation (exponent and prefactor) of the number of defects produced as a function of the rate of increase of the critical parameter. The procedure is valid in both the overdamped and underdamped limits. In one space dimension, we perform quantitative comparison with numerical simulations of the nonlinear nonautonomous stochastic partial differential equation and report on signatures of underdamped dynamics.
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