Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tunneling catastrophes of the partition function   We use path-integrals to derive a general expression for the semiclassical
approximation to the partition function of a one-dimensional quantum-mechanical
system. Our expression depends solely on ordinary integrals which involve the
potential. For high temperatures, the semiclassical expression is dominated by
single closed paths. As we lower the temperature, new closed paths may appear,
including tunneling paths. The transition from single to multiple-path regime
corresponds to well-defined catastrophes. Tunneling sets in whenever they
occur. Our formula fully accounts for this feature.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th