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 Ufimsk. Mat. Zh., 2009, Volume 1, Issue 3, Pages 3–10 (Mi ufa14)

Particle localization in a double-well potential and pseudo-supersymmetry

V. G. Bagrova, B. F. Samsonova, V. V. Shamshutdinovab

a Tomsk State University
b Tomsk Polytechnic University

Abstract: We show that a non-periodical smooth driving force can produce coherent destruction of tunnelling for a particle in a double-well potential having a couple of (lowest) energy levels very close to each other and well enough separated from the other levels (two-level approximation). An analysis of the time behavior of the occupation probability shows that the probability oscillates between a minimal value exceeding 1/2 and a maximal value close to 1. In particular, for specific parameter values of the driving force, it becomes a function monotonously increasing up to a value more then 1/2. These non-periodical external fields were obtained with the help of an extension of the transformation operator method to the case of a (non-Hermitian) Dirac-like Hamiltonian describing a two-level system. Two pseudosuperpartners and pseudosupersymmetry generators closing a quadratic pseudosuperalgebra were constructed. This allows us to conclude that a quadratic pseudosupersymmetry may be associated with the two-level system.

Keywords: exactly solvable models, Darboux transformation, pseudo-supersymmetry.

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Bibliographic databases:

UDC: 530.145

Citation: V. G. Bagrov, B. F. Samsonov, V. V. Shamshutdinova, “Particle localization in a double-well potential and pseudo-supersymmetry”, Ufimsk. Mat. Zh., 1:3 (2009), 3–10

Citation in format AMSBIB
\Bibitem{BagSamSha09} \by V.~G.~Bagrov, B.~F.~Samsonov, V.~V.~Shamshutdinova \paper Particle localization in a double-well potential and pseudo-supersymmetry \jour Ufimsk. Mat. Zh. \yr 2009 \vol 1 \issue 3 \pages 3--10 \mathnet{http://mi.mathnet.ru/ufa14} \zmath{https://zbmath.org/?q=an:1240.81017}