Controlling One-Dimensional Langevin Dynamics on the Lattice

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 ${\varphi }^4$ field theory as the application arena, we present such an analysis for a 1+1-dimensional Langevin system. Analytical predictions and results from high resolution numerical solutions are found to be in excellent agreement.

10 pages, 5 figures, uses RevTex

References in corpus (8)

• Discrete Breathers
• Mobility and Reactivity of Discrete Breathers
• Chern-Simons number diffusion with hard thermal loops
• Exact Thermodynamics of the Double sinh-Gordon Theory in 1+1-Dimensions
• Statistical Mechanics of Double sinh-Gordon Kinks
• Effective theory for real-time dynamics in hot gauge theories
• How to Count Kinks: From the Continuum to the Lattice and Back
• Real time simulations and the electroweak phase transition

Cited by in corpus (8)

• The Stochastic Gross-Pitaevskii Equation and some Applications
• Dynamics of Kinks: Nucleation, Diffusion and Annihilation
• Ab initio methods for finite temperature two-dimensional Bose gases
• Finite element discretization of non-linear diffusion equations with thermal fluctuations
• Langevin Simulation of Scalar Fields: Additive and Multiplicative Noises and Lattice Renormalization
• Langevin dynamics of the pure SU(2) deconfining transition
• Higher-order field theories: ${\varphi }^6$, ${\varphi }^8$ and beyond
• Stochastic Production Of Kink-Antikink Pairs In The Presence Of An Oscillating Background