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KRM

In the present article we prove an algebraic rate of decay towards the
equilibrium for the solution of a non-homogeneous, linear
kinetic transport
equation. The estimate is of the form
$C(1+t)^{-a}$ for some $a>0$. The total scattering
cross-section $R(k)$ is allowed to
degenerate but we assume that $R^{-a}(k)$ is integrable with respect
to the invariant measure.

DCDS-B

We consider energy fluctuations for solutions of the
Schrödinger equation with an Ornstein-Uhlenbeck random potential when the initial
data is spatially localized. The limit of the fluctuations of the Wigner transform
satisfies a kinetic equation with random initial data. This result generalizes that of [12]
where the random potential was assumed to be white noise in time.

KRM

We consider a one dimensional infinite chain of harmonic oscillators whose dynamics is weakly perturbed by a stochastic term conserving energy and momentum and whose evolution is governed by an Ornstein-Uhlenbeck process. We prove the kinetic limit for the Wigner functions corresponding to the chain. This result generalizes the results of [

keywords:
Harmonic oscillators
,
kinetic limit
,
Ornstein-Uhlenbeck process
,
Wigner functions
,
correctors

## Year of publication

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