States of a quantum particle exhibiting complex quasi-energy in a dynamic trap
States of a single quantum particle in a one-dimensional dynamic trap, which correspond to complex values of quasi-energy, are found. The trap is described by a square potential well with periodic smallamplitude oscillations of barrier position. The specific feature of the problem is the fact that the dynamic trap affords simultaneous localization and excitation of the confined particle. The complex nature of the quasienergy is caused by finite probability of particle escape from the trap due to finite depth of the potential well. Within the framework of the second-order perturbation theory with respect to modulation depth, the dependence of the decay rate of the states on modulation frequency is determined, which proves to be nonmonotonic.
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