Abstract
In this paper we show that in the semiclassical regime of periodic potential large enough, the Stark-Wannier ladders become a dense energy spectrum because of a cascade of bifurcations while increasing the ratio between the effective nonlinearity strength and the tilt of the external field; this fact is associated to a transition from regular to quantum chaotic dynamics. The sequence of bifurcation points is explicitly given.
Highlights
The dynamics of a quantum particle in a periodic potential under a homogeneous external field is one of the most important problems in solid-state physics
Because of the periodicity of the potential associated to the optical lattice, the existence of families of stationary states with associated energies displaced on regular ladders, the so-called Stark-Wannier ladders [10,11], is expected (see [12] for numerical computation of Stark-Wannier states for Bose-Einstein condensates (BECs) in an accelerated optical lattice); this picture implies, at least for a single-particle model, Bloch oscillations
Meinert et al [16] observed that when the strength of the uniform acceleration is reduced a transition from regular to quantum chaotic dynamics is observed; in their experiments evidence of the fact that the energy spectrum emerges densely packed, as predicted by [17] by means of a numerical simulation for a lattice with a finite number of wells, is given
Summary
The dynamics of a quantum particle in a periodic potential under a homogeneous external field is one of the most important problems in solid-state physics.
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