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Localization of an particle in two-hole potential and pseudosupersymmetry. (Russian. English summary) Zbl 1240.81017
The authors show the detection possibility of coherent destruction of tunnelling in two-level approximation in two-hole potential on account of interaction of non-periodical smooth perturbations. An analysis of tunnelling probability behavior shows that this probability oscillates between some minimal value which can exceed 1/2 and a maximal value which can approach 1. When the perturbating parameters are in the vicinity of some critical values, smoothing of oscillations occurs. As a result, this probability becomes a monotone, increasing-in-time function up to some limit value which can exceed 1/2. Such aperiodic perturbations are obtained on the base of the transformation operators as a generalization of the Dirac system with non-Hermitian effective Hamiltonian describing the evolution of the two-level system. In the article, supercharges and super-Hamiltonian are constructed closing a quadratic pseudosuperalgebra, which allows to connect this detected effect with the existence of supersymmetry in the two-level system.
81Q15 Perturbation theories for operators and differential equations in quantum theory
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