Volume 118, Number 2, April 2017
|Number of page(s)||7|
|Published online||21 June 2017|
Rapidly oscillating scatteringless non-Hermitian potentials and the absence of Kapitza stabilization
Dipartimento di Fisica, Politecnico di Milano - Piazza L. da Vinci 32, I-20133 Milano, Italy and Istituto di Fotonica e Nanotecnlogie del Consiglio Nazionale delle Ricerche, sezione di Milano Piazza L. da Vinci 32, I-20133 Milano, Italy
Received: 10 February 2017
Accepted: 26 May 2017
In the framework of the ordinary non-relativistic quantum mechanics, it is known that a quantum particle in a rapidly oscillating bound potential with vanishing time average can be scattered off or even trapped owing to the phenomenon of dynamical (Kapitza) stabilization. A similar phenomenon occurs for scattering and trapping of optical waves. Such a remarkable result stems from the fact that, even though the particle is not able to follow the rapid external oscillations of the potential, these are still able to affect the average dynamics by means of an effective —albeit small— nonvanishing potential contribution. Here we consider the scattering and dynamical stabilization problem for matter or classical waves by a bound potential with oscillating ac amplitude f(t) in the framework of a non-Hermitian extension of the Schrödinger equation, and predict that for a wide class of imaginary amplitude modulations f(t) possessing a one-sided Fourier spectrum, the oscillating potential is effectively canceled, i.e., it does not have any effect on the particle dynamics, contrary to what happens in the Hermitian case.
PACS: 03.65.Nk – Scattering theory / 03.65.-w – Quantum mechanics
© EPLA, 2017
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