Effective potential for non-coupled stochastic partial differential equations

• Pedro Franceschini Universidad del Zulia, Centro de Modelado Científico (CMC)
• Luís González Universidad del Zulia, Centro de Modelado Científico (CMC)
• íngel Muñoz Universidad del Zulia, Laboratorio de Astronomía y Física Teórica (LAFT), Departamento de Física, Facultad de Ciencias
• David Sierra Porta Universidad del Zulia, Laboratorio de Astronomía y Física Teórica (LAFT), Departamento de Física, Facultad de Ciencias
• Terenzio Soldovieri Universidad del Zulia, Laboratorio de Astronomía y Física Teórica (LAFT), Departamento de Física, Facultad de Ciencias

Palabras clave: stochastic partial differential equations, effective potential

Resumen

We provide an Effective Potential Formulation for non-coupled (i.e. independent) Stochastic Partial Differential Equations with additive noise using the Hojman et al. method for writing the associated Lagrangean function. We show that this Potential is able to reproduce all the dynamics of the system, once a special differential operator has been applied. This procedure can be used to study the equilibria cases, the complete time evolution and spatial inhomogeneities of the system under consideration