Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stationary scattering theory for $1$-body Stark operators, II   We study and develop the stationary scattering theory for a class of one-body
Stark Hamiltonians with short-range potentials, including the Coulomb
potential, continuing our study in [AIIS1,AIIS2]. The classical scattering
orbits are parabolas parametrized by asymptotic orthogonal momenta, and the
kernel of the (quantum) scattering matrix at a fixed energy is defined in these
momenta. We show that the scattering matrix is a classical type
pseudodifferential operator and compute the leading order singularities at the
diagonal of its kernel. Our approach can be viewed as an adaption of the method
of Isozaki-Kitada [IK] used for studying the scattering matrix for one-body
Schr\"odinger operators without an external potential. It is more flexible and
more informative than the more standard method used previously by
Kvitsinsky-Kostrykin [KK1] for computing the leading order singularities of the
kernel of the scattering matrix in the case of a constant external field (the
Stark case). Our approach relies on Sommerfeld's uniqueness result in Besov
spaces, microlocal analysis as well as on classical phase space constructions.

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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph