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

• Model of accelerated ultracold condensate in optical lattices.
• Numerical computation of wavefunction of condensates.
• Numerical computation of the oscillating period of the center of mass of condensates.

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 Schrödinger 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.