Dynamics of defect formation
Physical Review E
59 R1303-1306 (1999)
Departmento de Mathematicas, Universidad Carlos III de Madrid.
E-28911 Leganes, Madrid, SPAIN.
Centre for Nonlinear Studies
Los Alamos National Laboratory
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.