Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodicity for the weakly damped stochastic non-linear Schr\"{o}dinger
  equations   We study a damped stochastic non-linear Schr\"{o}dinger (NLS) equation driven
by an additive noise. It is white in time and smooth in space. Using a coupling
method, we establish convergence of the Markovian transition semi-group toward
a unique invariant probability measure. This kind of method was originally
developped to prove exponential mixing for strongly dissipative equations such
as the Navier-Stokes equations. We consider here a weakly dissipative equation,
the damped nonlinear Schr\"{o}dinger equation in the one dimensional cubic
case. We prove that the mixing property holds and that the rate of convergence
to equilibrium is at least polynomial of any power.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex