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
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.
exactly solvable models, Darboux transformation, pseudo-supersymmetry.
PDF file (724 kB)
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
\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.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|