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Matematicheskie Zametki, 2017, Volume 102, Issue 6, paper published in the English version journal (Mi mzm11823)  

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

Papers published in the English version of the journal

Instantons via Breaking Geometric Symmetry in Hyperbolic Traps

M. V. Karasev, E. M. Novikova, E. V. Vybornyi

National Research University Higher School of Economics, Laboratory for Mathematical Methods in Natural Sciences, Moscow, Russia
Citations (2)
Abstract: Using geometrical and algebraic ideas, we study tunnel eigenvalue asymptotics and tunnel bilocalization of eigenstates for certain class of operators (quantum Hamiltonians) including the case of Penning traps, well known in physical literature. For general hyperbolic traps with geometric asymmetry, we study resonance regimes which produce hyperbolic type algebras of integrals of motion. Such algebras have polynomial (non-Lie) commutation relations with creation-annihilation structure. Over this algebra, the trap asymmetry (higher-order anharmonic terms near the equilibrium) determines a pendulum-like Hamiltonian in action-angle coordinates. The symmetry breaking term generates a tunneling pseudoparticle (closed instanton). We study the instanton action and the corresponding spectral splitting.
Keywords: frequency resonance, polynomial algebra, Penning trap, symplectic instanton, tunnel splitting.
Funding agency Grant number
HSE Basic Research Program
This work was supported by the Program for Fundamental Research of Higher School of Economics.
Received: 09.10.2017
English version:
Mathematical Notes, 2017, Volume 102, Issue 6, Pages 776–786
DOI: https://doi.org/10.1134/S0001434617110177
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. V. Karasev, E. M. Novikova, E. V. Vybornyi, “Instantons via Breaking Geometric Symmetry in Hyperbolic Traps”, Math. Notes, 102:6 (2017), 776–786
Citation in format AMSBIB
\Bibitem{KarNovVyb17}
\by M.~V.~Karasev, E.~M.~Novikova, E.~V.~Vybornyi
\paper Instantons via Breaking Geometric Symmetry in Hyperbolic Traps
\jour Math. Notes
\yr 2017
\vol 102
\issue 6
\pages 776--786
\mathnet{http://mi.mathnet.ru/mzm11823}
\crossref{https://doi.org/10.1134/S0001434617110177}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000418838500017}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85039436497}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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