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Matematicheskie Zametki, 2017, Volume 102, Issue 6, paper published in the English version journal
(Mi mzm11823)
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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
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.
Received: 09.10.2017
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
Linking options:
https://www.mathnet.ru/eng/mzm11823
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