Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Properties of the Langevin and Fokker-Planck equations for scalar fields
  and their application to the dynamics of second order phase transitions   I consider several Langevin and Fokker-Planck classes of dynamics for scalar
field theories in contact with a thermal bath at temperature T. These models
have been applied recently in the numerical description of the dynamics of
second order phase transitions and associated topological defect formation as
well as in other studies of these critical phenomena. Closed form solutions of
the Fokker-Planck equation are given for the harmonic potential and a dynamical
mean-field approximation is developed. These methods allow for an analytical
discussion of the behavior of the theories in several circumstances of interest
such as critical slowing down at a second order transition and the development
of spinodal instabilities. These insights allow for a more detailed
understanding of several numerical studies in the literature.

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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom