NOISE and ULTRAVIOLET DIVERGENCES IN SIMULATIONS of GINZBURG-LANDAU-LANGEVIN TYPE of EQUATIONS - Cassol-Seewald, N. C. [UNESP]; Farias, R. L. S.; Krein, Gastão Inácio [UNESP]; Marques de Carvalho, R. S. (World Scientific Publ Co Pte Ltd, 2012)
The time evolution of an order parameter towards equilibrium can be described by nonlinear Ginzburg-Landau (GL) type of equations, also known as time-dependent nonlinear Schrodinger equations. Environmental effects of random nature are usually taken into account by noise sources, turning the GL equations into stochastic equations. Noise sources give rise to lattice-spacing 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 field theory and stochastic quantization.
Keywords: Dynamical phase transitions; stochastic quantization