Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tunnel effect for Kramers-Fokker-Planck type operators: return to
  equilibrium and applications   In the first part of this work, we consider second order supersymmetric
differential operators in the semiclassical limit, including the
Kramers-Fokker-Planck operator, such that the exponent of the associated
Maxwellian $\phi$ is a Morse function with two local minima and one saddle
point. Under suitable additional assumptions of dynamical nature, we establish
the long time convergence to the equilibrium for the associated heat semigroup,
with the rate given by the first non-vanishing, exponentially small,
eigenvalue. In the second part of the paper, we consider the case when the
function $\phi$ has precisely one local minimum and one saddle point. We also
discuss further examples of supersymmetric operators, including the Witten
Laplacian and the infinitesimal generator for the time evolution of a chain of
classical anharmonic oscillators.

37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph