Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical time evolution of the density matrix and tunneling   The time dependent density matrix of a system with potential barrier is
studied using path integrals. The characterization of the initial state, which
is assumed to be restricted to one side of the barrier, and the time evolution
of the density matrix lead to a three-fold path integral which is evaluated in
the semiclassical limit. The semiclassical trajectories are found to move in
the complex coordinate plane and barrier penetration only arises due to
fluctuations. Both the form of the semiclassical paths and the relevant
fluctuations change significantly as a function of temperature. The
semiclassical analysis leads to a detailed picture of barrier penetration in
the real time domain and the changeover from thermal activation to quantum
tunneling. Deep tunneling is associated with quasi-zero modes in the
fluctuation spectrum about the semiclassical orbits in the long time limit. The
connection between this real time description of tunneling and the standard
imaginary time instanton approach is established. Specific results are given
for a double well potential and an Eckart barrier.

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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: econ