Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Return to Equilibrium for an Anharmonic Oscillator coupled to a Heat
  Bath   We study a $C^*$-dynamical system describing a particle coupled to an
infinitely extended heat bath at positive temperature. For small coupling
constant we prove return to equilibrium exponentially fast in time. The novelty
in this context is to model the particle by a harmonic or anharmonic
oscillator, respectively. The proof is based on explicit formulas for the time
evolution of Weyl operators in the harmonic oscillator case. In the anharmonic
oscillator case, a Dyson's expansion for the dynamics is essential. Moreover,
we show in the harmonic oscillator case, that $\R$ is the absolute continuous
spectrum of the Standard Liouvillean and that zero is a unique eigenvalue.

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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int