Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field

Melgaard, Michael (2003) Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field. Central European Journal of Mathematics, 1 (4). pp. 477-509. ISSN 1895-1074

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Abstract

For fixed magnetic quantum number $m$ results on spectral properties and scattering theory are given for the three-dimensional Schrödinger operator with a constant magnetic field and an axisymmetrical electric potential $V$.
In various, mostly fairly singular settings asymptotic expansions for the
resolvent of the Hamiltonian $H_{m}=H_{om}+V$ are deduced as the spectral
parameter tends to the lowest Landau threshold. Furthermore, scattering theory
for the pair $(H_{m}, H_{om})$ is established and asymptotic expansions of the
scattering matrix are derived as the energy parameter tends to the lowest
Landau threshold

Item Type: Article
Keywords: Near-threshold resolvent expansions; scattering matrix; auxiliary one-dimensional Schrödinger operator
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
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Depositing User: Michael Melgaard
Date Deposited: 19 Sep 2013 13:27
Last Modified: 19 Sep 2013 13:27
URI: http://sro.sussex.ac.uk/id/eprint/46389
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