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Matematicheskie Zametki, 2022, Volume 112, Issue 5, Pages 752–769
DOI: https://doi.org/10.4213/mzm13776
(Mi mzm13776)
 

This article is cited in 2 scientific papers (total in 2 papers)

On the Delocalization of a Quantum Particle under the Adiabatic Evolution Generated by a One-Dimensional Schrödinger Operator

V. A. Sergeevab, A. A. Fedotova

a Saint Petersburg State University
b Euler International Mathematical Institute, St. Petersburg
Full-text PDF (644 kB) Citations (2)
References:
Abstract: The one-dimensional nonstationary Schrödinger equation is discussed in the adiabatic approximation. The corresponding stationary operator HH, depending on time as a parameter, has a continuous spectrum σc=[0,+) and finitely many negative eigenvalues. In time, the eigenvalues approach the edge of σc and disappear one by one. The solution under consideration is close at some moment to an eigenfunction of H. As long as the corresponding eigenvalue λ exists, the solution is localized inside the potential well. Its delocalization with the disappearance of λ is described.
Keywords: one-dimensional nonstationary Schrödinger operator, delocalization of a quantum state, adiabatic evolution.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00451 А
This work was supported by the Russian Foundation for Basic Research under grant 20-01-00451 A.
Received: 07.06.2022
Revised: 26.06.2022
English version:
Mathematical Notes, 2022, Volume 112, Issue 5, Pages 726–740
DOI: https://doi.org/10.1134/S0001434622110098
Bibliographic databases:
Document Type: Article
UDC: 51.73
Language: Russian
Citation: V. A. Sergeev, A. A. Fedotov, “On the Delocalization of a Quantum Particle under the Adiabatic Evolution Generated by a One-Dimensional Schrödinger Operator”, Mat. Zametki, 112:5 (2022), 752–769; Math. Notes, 112:5 (2022), 726–740
Citation in format AMSBIB
\Bibitem{SerFed22}
\by V.~A.~Sergeev, A.~A.~Fedotov
\paper On the Delocalization of a Quantum Particle under the Adiabatic Evolution Generated by a One-Dimensional Schr\"odinger Operator
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 5
\pages 752--769
\mathnet{http://mi.mathnet.ru/mzm13776}
\crossref{https://doi.org/10.4213/mzm13776}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538803}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 5
\pages 726--740
\crossref{https://doi.org/10.1134/S0001434622110098}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85145899334}
Linking options:
  • https://www.mathnet.ru/eng/mzm13776
  • https://doi.org/10.4213/mzm13776
  • https://www.mathnet.ru/eng/mzm/v112/i5/p752
  • This publication is cited in the following 2 articles:
    1. V. A. Sergeev, A. A. Fedotov, “O poverkhnostnoi volne, voznikayuschei posle delokalizatsii kvantovoi chastitsy pri adiabaticheskoi evolyutsii”, Algebra i analiz, 36:1 (2024), 204–233  mathnet
    2. V.A. Sergeev, “On the Upslope Propagation of an Adiabatic Normal Mode in a Wedge-Shaped Sea”, Russ. J. Math. Phys., 31:2 (2024), 308  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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