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TMF, 2003, Volume 136, Number 3, Pages 507–516 (Mi tmf1915)  

This article is cited in 4 scientific papers (total in 4 papers)

Mathematical Model of Resonances and Tunneling in a System with a Bound State

A. A. Arsen'ev

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We study the asymptotic behavior of the residue at the pole of the analytic continuation of the scattering matrix as the imaginary part of the pole tends to zero in the case where the phase space of a quantum mechanical system is a direct sum of two spaces and the nonperturbed evolution operator reduces each of these spaces and has a discrete spectrum in one of them and a continuous spectrum in the other. The perturbation operator mixes the subspaces and generates a resonance. We prove that under certain symmetry conditions in such a system, the scattering amplitude changes sharply in a neighborhood of the real part of the pole of the scattering matrix, and the system demonstrates tunneling or a resonance of the scattering amplitude.

Keywords: scattering, resonance, tunneling

DOI: https://doi.org/10.4213/tmf1915

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English version:
Theoretical and Mathematical Physics, 2003, 136:3, 1336–1345

Bibliographic databases:

Received: 21.01.2003

Citation: A. A. Arsen'ev, “Mathematical Model of Resonances and Tunneling in a System with a Bound State”, TMF, 136:3 (2003), 507–516; Theoret. and Math. Phys., 136:3 (2003), 1336–1345

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Arsen'ev, “Resonances and Tunneling in the Tight-Binding Approximation to Scattering in a Quantum Billiard”, Theoret. and Math. Phys., 141:1 (2004), 1415–1426  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. A. A. Arsen'ev, “Resonances and tunneling in a quantum wire”, Theoret. and Math. Phys., 147:1 (2006), 524–532  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. A. Arsen'ev, “Tunneling through a quantum dot in a quantum waveguide”, Comput. Math. Math. Phys., 50:7 (2010), 1162–1171  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    4. Belov P.A., “Energy Spectrum of Excitons in Square Quantum Wells”, Physica E, 112 (2019), 96–108  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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