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On resonances and bound states of Smilansky Hamiltonian
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SYSNO ASEP 0466593 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On resonances and bound states of Smilansky Hamiltonian Author(s) Exner, Pavel (UJF-V) RID, ORCID, SAI
Lotoreichik, Vladimir (UJF-V) ORCID, SAI
Tater, Miloš (UJF-V) RID, ORCID, SAINumber of authors 3 Source Title Nanosystems: Physics, Chemistry, Mathematics - ISSN 2220-8054
Roč. 7, č. 5 (2016), s. 789-802Number of pages 14 s. Publication form Print - P Language eng - English Country RU - Russian Federation Keywords Smilansky Hamiltonian ; resonances ; resonance free region ; weak coupling asymptotics ; Riemann surface ; bound states Subject RIV BE - Theoretical Physics R&D Projects GA14-06818S GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000387463700002 DOI 10.17586/2220-8054-2016-7-5-789-802 Annotation We consider the self-adjoint Smilansky Hamiltonian H epsilon in L-2(R-2) associated with the formal differential expression -partial derivative(2)(x) - 1/2 (partial derivative(2)(y) + y(2)) - root 2 epsilon y delta(x) in the sub-critical regime, epsilon is an element of (0, 1). We demonstrate the existence of resonances for H-epsilon on a countable subfamily of sheets of the underlying Riemann surface whose distance from the physical sheet is finite. On such sheets, we find resonance free regions and characterize resonances for small epsilon > 0. In addition, we refine the previously known results on the bound states of H " in the weak coupling regime (epsilon -> 0+). In the proofs we use Birman-Schwinger principle for H-epsilon, elements of spectral theory for Jacobi matrices, and the analytic implicit function theorem. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2017
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