The Gaussian effective potential and stochastic partial differential equations

✍ Scribed by F.S. Amaral; I. Roditi

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 202 KB
• Volume: 385
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2007.06.035

✦ Synopsis

We investigate arbitrary stochastic partial differential equations subject to translation invariant and temporally white noise correlations from a nonperturbative framework. The method that we expose first casts the stochastic equations into a functional integral form, then it makes use of the Gaussian effective potential approach, which is an useful tool for describing symmetry breaking. We apply this method to the Kardar-Parisi-Zhang equation and find that the system exhibits spontaneous symmetry breaking in ð1 þ 1Þ; ð2 þ 1Þ and ð3 þ 1Þ Euclidean dimensions, providing insight into the evolution of the system configuration due to the presence of noise correlations. A simple and systematic approach to the renormalization, without explicit regularization, is employed.