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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 181, Number 2, Pages 337–348
DOI: https://doi.org/10.4213/tmf8771 (Mi tmf8771) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Energy splitting in dynamical tunneling

E. V. Vybornyi

Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, Moscow, Russia
Full-text PDF (423 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf8771
Abstract: We propose an operator method for calculating the semiclassical asymptotic form of the energy splitting value in the general case of tunneling between symmetric orbits in the phase space. We use this approach in the case of a particle on a circle to obtain the asymptotic form of the energy tunneling splitting related to the over-barrier reflection from the potential. As an example, we consider the quantum pendulum in the rotor regime.
Keywords: dynamical tunneling, tunneling splitting, Schrödinger equation, semiclassical approximation, over-barrier reflection.
Received: 17.07.2014
English version:
Theoretical and Mathematical Physics, 2014, Volume 181, Issue 2, Pages 1418–1427
DOI: https://doi.org/10.1007/s11232-014-0222-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. V. Vybornyi, “Energy splitting in dynamical tunneling”, TMF, 181:2 (2014), 337–348; Theoret. and Math. Phys., 181:2 (2014), 1418–1427
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf8771
  • https://doi.org/10.4213/tmf8771
  • https://www.mathnet.ru/eng/tmf/v181/i2/p337
    • This publication is cited in the following 8 articles:
    1. Sofia V. Rumyantseva, “Asymptotic Expansion of Solutions of the 2nd Order Difference Equations in an Unbounded Domain”, Acta Appl Math, 195:1 (2025)  crossref
    2. E. V. Vybornyi, S. V. Rumyantseva, “Semiclassical Asymptotics of Oscillating Tunneling for a Quadratic Hamiltonian on the Algebra su(1,1)”, Math. Notes, 112:5 (2022), 642–655  mathnet  crossref  crossref  mathscinet
    3. A. Yu. Anikin, J. Bruening, S. Yu. Dobrokhotov, E. V. Vybornyi, “Averaging and spectral bands for the 2-D magnetic Schrodinger operator with growing and one-direction periodic potential”, Russ. J. Math. Phys., 26:3 (2019), 265–276  crossref  mathscinet  isi
    4. M. Karasev, E. Vybornyi, “Bi-orbital states in hyperbolic traps”, Russ. J. Math. Phys., 25:4 (2018), 500–508  crossref  mathscinet  zmath  isi  scopus
    5. M. V. Karasev, E. M. Novikova, E. V. Vybornyi, “Instantons via Breaking Geometric Symmetry in Hyperbolic Traps”, Math. Notes, 102:6 (2017), 776–786  mathnet  mathnet  crossref  isi  scopus
    6. M. V. Karasev, E. M. Novikova, E. V. Vybornyi, “Non-Lie Top Tunneling and Quantum Bilocalization in Planar Penning Trap”, Math. Notes, 100:6 (2016), 807–819  mathnet  mathnet  crossref  isi  scopus
    7. Lars Ackermann, Stefan Schönig, Stefan Jablonski, Lecture Notes in Business Information Processing, 272, Enterprise and Organizational Modeling and Simulation, 2016, 3  crossref
    8. Dong Ch., Wang L., Zhao K., “Embedded Mobile Crowd Service Systems Based on Opportunistic Geological Grid and Dynamical Segmentation”, EURASIP J. Embed. Syst., 2015, no. 1, 3  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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