Abstract

SANJINES C., Diego. A CRITERION FOR DYNAMIC LOCALIZATION BASED ON THE KAPITZA PENDULUM SCHEME IN THE LATTICE. Revista Boliviana de Física [online]. 2013, vol.22, n.22, pp.14-20. ISSN 1562-3823.

We propose a scheme to choose a quantum potential of the form V(x,t)=V(x)−∫dxf(x,t) that yields dynamic localization of a particle moving in a one dimensional crystal within the tight-binding model. A time-independent effective potential V_ef(x) corresponding to V(x,t) is obtained by means of a formula deduced from the classical theory of the Kapitza pendulum for large frequencies of the force f(x,t) ([82005Gallinar]). If the solutions x(t) of the semiclassical equations of motion (corresponding to V_ef(x)) are confined according to the [101972Kroopnick] theorem then we propose the conjecture that confinement implies quantum localization. This conjecture is confirmed for some potentials V(x,t) obeying the Kroopnick criterion. We analize in particular the case of potentials of the form V(x,t)=xF(t) which are associated to dynamic localization.

Keywords : Semiclassical theories and applications; hopping transport; transport theory.

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