We consider the Langevin lattice dynamics for a spontaneously broken λφ 4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg-Landau-Langevin and the subtleties related to the multiplicative noise are investigated.

No abstract

The time evolution of an order parameter towards equilibrium can be described by nonlinear GinzburgÀLandau (GL) type of equations, also known as time-dependent nonlinear Schr€ odinger equations. Environmental e®ects of random nature are usually taken into account by noise sources, turning the GL equations into stochastic equations. Noise sources give rise to latticespacing dependence of the solutions of the stochastic equations. We present a systematic method to renormalize the equations on a spatial lattice to obtain lattice-spacing independent solutions. We illustrate the method in approximation schemes designed to treat nonlinear and nonlocal GL equations that appear in real time thermal¯eld theory and stochastic quantization.

The nonequilibrium effective equation of motion for a scalar background field in a thermal bath is studied numerically. This equation emerges from a microscopic quantum field theory derivation and it is suitable to a Langevin simulation on the lattice. Results for both the symmetric and broken phases are presented.Comment: To appear in the proceedings of 5th International Conference on Perspectives in Hadronic Physics: International Conference on Particle-Nucleus and Nucleus-Nucleus Scattering at Relativistic Energies, Trieste, Italy, 22-26 May 2006. V2:reference correcte

This work is concerned with non-equilibrium phenomena, with focus on the numerical simulation of the relaxation of non-conserved order parameters described by stochastic kinetic equations known as GinzburgLandau-Langevin (GLL) equations. We propose methods for solving numerically these type of equations, with additive and multiplicative noises. Illustrative applications of the methods are presented for different GLL equations, with emphasis on equations incorporating memory effects.