Controlling One-Dimensional Langevin Dynamics on the Lattice
Physical Review D
60 105039 (1999)
Luis Bettencourt and Salman Habib
T8
Los Alamos National Laboratory
NM87545, USA.
G.D. Lythe
Centre for Nonlinear Studies
Los Alamos National Laboratory
NM87545, USA.
Abstract
Stochastic evolutions of classical field theories have recently become
popular in the study of problems such as determination of the rates of
topological transitions and the statistical mechanics of nonlinear
coherent structures. To obtain high precision results from numerical
calculations, a careful accounting of spacetime discreteness effects
is essential, as well as the development of schemes to systematically
improve convergence to the continuum. With a kink-bearing Ø4
field theory as the application arena, we present such an analysis for
a 1+1-dimensional Langevin system. High resolution numerical
results provide excellent supporting evidence for our
analytical predictions.