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Noise And Ultraviolet Divergences In Simulations Of Ginzburg–Landau–Langevin Type Of Equations

Author

Listed:
  • N. C. CASSOL-SEEWALD

    (Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271 — Bloco II, 01140-070 — São Paulo, SP, Brazil)

  • R. L. S. FARIAS

    (Departamento de Ciências Naturais, Universidade Federal de São João Del Rei, 36301-000 — São João Del Rei, MG, Brazil)

  • G. KREIN

    (Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271 — Bloco II, 01140-070 — São Paulo, SP, Brazil)

  • R. S. MARQUES DE CARVALHO

    (Departamento de Informática em Saúde, Escola Paulista de Medicina — UNIFESP, Rua Botucatu, 862 — Térreo, 04023-062 — São Paulo, SP, Brazil)

Abstract

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 Schrödinger 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.

Suggested Citation

  • N. C. Cassol-Seewald & R. L. S. Farias & G. Krein & R. S. Marques De Carvalho, 2012. "Noise And Ultraviolet Divergences In Simulations Of Ginzburg–Landau–Langevin Type Of Equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 23(08), pages 1-9.
    • Handle: RePEc:wsi:ijmpcx:v:23:y:2012:i:08:n:s0129183112400165
    DOI: 10.1142/S0129183112400165
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