Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

Hochberg, David; Molina-Parı́s, Carmen; Visser, Matt

doi:10.1103/physreve.63.036132

Cited by 1 publication

(2 citation statements)

References 34 publications

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“…As reported [9,16], in other approaches the effective potential is useful only for stationary or static regimes; the approach presented here can be used to study those cases, the complete temporal evolution of (1) and also the equilibria and stability states. The present potential formulation is based on a classical mechanics approach, there is no need of auxiliary or ghost fields.…”

Section: The Hojman Et Al Methods Enables Us To Writementioning

confidence: 99%

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Variational and potential formulation for stochastic partial differential equations

Munoz¹,

Ojeda²,

Sierra³

et al. 2006

J. Phys. A: Math. Gen.

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There is recent interest in finding a potential formulation for Stochastic Partial Differential Equations (SPDEs). The rationale behind this idea lies in obtaining all the dynamical information of the system under study from one single expression. In this Letter we formally provide a general Lagrangian formalism for SPDEs using the Hojman et al. method. We show that it is possible to write the corresponding effective potential starting from an s-equivalent Lagrangean, and 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 complete time evolution and spatial inhomogeneities of the system under consideration, and is also suitable for the statistical mechanics description of the problem. The inverse problem of variational calculus have been used by Hojman et al. [1] in the study of systems associated with first and second order deterministic differential equations. The propoused method permits to obtain all the dynamical infomation of the system allowing the quantization in terms of conserved quantities prescibed for the differential equation. On the other hand, a variational formalism has been devised by Gambár and Márkus (see for example [2, 3, 4]) as groundwork for proposing a field theory for nonequilibrium thermodynamical systems, giving valuable information about the entropy in terms of current density and thermodynamic forces. Effective actions can be found by means of the Martin-Siggia-Rose formalism [5], a perturbative procedure that makes use of both physical and "conjugate" (auxiliary) fields. Also, Hochberg et al. have proposed in a series of papers [6,7,8] a "direct" approach, finding effective actions and potentials for SPDEs using a functional integral formalism similar in structure to those of quantum field theory. Last year Ao [9] has reported a worth consulting novel approach for constructing potentials associated with first order SPDEs. All this efforts conduct to the idea that the variational formalism, in its direct or inverse form, could be the mathematical mechanism with the necessary tools for exploring the inherent dynamics of physical, biological and chemical systems. In particular, structural development in cosmology and biology, pattern-formation, symmetry breaking, *

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Section: The Hojman Et Al Methods Enables Us To Writementioning

confidence: 99%

“…In a more recent paper [16] Hochberg et al have reported that their effective potential does not provide information about the time evolution and spatial inhomogeneities of the system under consideration, and the effective action is very difficult to calculate exactly.…”

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confidence: 99%