Localization of an particle in two-hole potential and pseudosupersymmetry.

*(Russian. English summary)*Zbl 1240.81017The 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.

Reviewer: Boris V. Loginov (Ul’yanovsk)

##### MSC:

81Q15 | Perturbation theories for operators and differential equations in quantum theory |