Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on Harris' ergodic theorem, controllability and perturbations of
  harmonic networks   We show that elements of control theory, together with an application of
Harris' ergodic theorem, provide an alternate method for showing exponential
convergence to a unique stationary measure for certain classes of networks of
quasi-harmonic classical oscillators coupled to heat baths. With the system of
oscillators expressed in the form $\mathrm{d} X_t = A X_t \,\mathrm{d} t +
F(X_t) \,\mathrm{d} t + B \,\mathrm{d} W_t$ in $\mathbf{R}^d$, where $A$
encodes the harmonic part of the force and $-F$ corresponds to the gradient of
the anharmonic part of the potential, the hypotheses under which we obtain
exponential mixing are the following: $A$ is dissipative, the pair $(A,B)$
satisfies the Kalman condition, $F$ grows sufficiently slowly at infinity
(depending on the dimension $d$), and the vector fields in the equation of
motion satisfy the weak H\"ormander condition in at least one point of the
phase space.

13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs