Nonlinear Schrodinger equations with a multiple-well potential and a Stark-type perturbation

作者：Sacchetti Andrea^*

来源：Physica D: Nonlinear Phenomena , 2016, 321: 39-50.

DOI：10.1016/j.physd.2016.02.016

• Bose-Einstein condensates
• Gross-Pitaevskii equations
• Bloch oscillations

A Bose Einstein condensate (BEC) confined in a one-dimensional lattice under the effect of an external homogeneous field is described by the Gross-Pitaevskii equation. Here we prove that such an equation can be reduced, in the semiclassical limit and in the case of a lattice with a finite number of wells, to a finite-dimensional discrete nonlinear Schrodinger equation. Then, by means of numerical experiments we show that the BEC's center of mass exhibits an oscillating behavior with modulated amplitude; in particular, we show that the oscillating period actually depends on the shape of the initial wavefunction of the condensate as well as on the strength of the nonlinear term. This fact opens a question concerning the validity of a method proposed for the determination of the gravitational constant by means of the measurement of the oscillating period.

• 出版日期2016-5-1