Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The tunneling splitting and the Kramers theory of activated processes   The study of tunneling splitting is fundamental to get insight into the
dynamics of a multitude of molecular systems. In this paper, a novel approach
to the analysis of the ground-state tunneling splitting is presented and
explicitly applied to one-dimensional systems. The isomorphism between the
Fokker-Planck-Smoluchowski operator and the Born-Oppenheimer quantum
Hamiltonian is the key element of this method. The localization function
approach, used in the field of stochastic processes to study the Kramers
problem, leads to a simple, yet asymptotically justified, integral
approximation for the tunneling splitting. The comparison with exact values of
the tunneling splittings shows a much better accuracy than WKB semiclassical
estimates.

6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ