Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp spectral asymptotics for non-reversible metastable diffusion
  processes   Let $U_h:\mathbb R^{d}\to \mathbb R^{d}$ be a smooth vector field and
consider the associated overdamped Langevin equation
$$dX_t=-U_h(X_t)\,dt+\sqrt{2h}\,dB_t$$ in the low temperature regime
$h\rightarrow 0$. In this work, we study the spectrum of the associated
diffusion $L=-h\Delta+U_h\cdot\nabla$ under the assumptions that
$U_h=U_{0}+h\nu$, where the vector fields $U_{0}:\mathbb R^{d}\to \mathbb
R^{d}$ and $\nu:\mathbb R^{d}\to \mathbb R^{d}$ are independent of $h\in(0,1]$,
and that the dynamics admits $e^{-\frac Vh}$ as an invariant measure for some
smooth function $V:\mathbb{R}^d\rightarrow\mathbb{R}$. Assuming additionally
that $V$ is a Morse function admitting $n_0$ local minima, we prove that there
exists $\epsilon>0$ such that in the limit $h\to 0$, $L$ admits exactly $n_0$
eigenvalues in the strip $\{0\leq \operatorname{Re}(z)< \epsilon\}$, which have
moreover exponentially small moduli. Under a generic assumption on the
potential barriers of the Morse function $V$, we also prove that the asymptotic
behaviors of these small eigenvalues are given by Eyring-Kramers type formulas.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
18
The categories of this paper are: econ
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat