The Gaussian effective potential and stochastic partial differential equations

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 Gauss...

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Bibliographic Details
Published inPhysica A Vol. 385; no. 1; pp. 137 - 147
Main Authors Amaral, F.S., Roditi, I.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2007
Subjects
Gaussian effective potential
KPZ equation
Stochastic equations
Stochastic equations
KPZ equation
Gaussian effective potential
03.70. + k
05.40. - a
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Summary: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 ( 1 + 1 ) , ( 2 + 1 ) and ( 3 + 1 ) 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.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2007.06.035