Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical study of shape resonances in the Stark effect   Semiclassical behavior of Stark resonances is studied. The complex distortion
outside a cone is introduced to study resonances in any energy region for the
Stark Hamiltonians with non-globally analytic potentials. The non-trapping
resolvent estimate is proved by the escape function method. The Weyl law and
the resonance expansion of the propagator are proved in the shape resonance
model. To prove the resonance expansion theorem, the functional
pseudodifferential calculus in the Stark effect is established, which is also
useful in the study of the spectral shift function.

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The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
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The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ