11 research outputs found
Disordered Bose Einstein Condensates with Interaction in One Dimension
We study the effects of random scatterers on the ground state of the
one-dimensional Lieb-Liniger model of interacting bosons on the unit interval
in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation
survives even a strong random potential with a high density of scatterers. The
character of the wave function of the condensate, however, depends in an
essential way on the interplay between randomness and the strength of the
two-body interaction. For low density of scatterers or strong interactions the
wave function extends over the whole interval. High density of scatterers and
weak interaction, on the other hand, leads to localization of the wave function
in a fragmented subset of the interval
Spreading of waves in nonlinear disordered media
We analyze mechanisms and regimes of wave packet spreading in nonlinear
disordered media. We predict that wave packets can spread in two regimes of
strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion
equations, and predict a dynamical crossover from strong to weak chaos. The
crossover is controlled by the ratio of nonlinear frequency shifts and the
average eigenvalue spacing of eigenstates of the linear equations within one
localization volume. We consider generalized models in higher lattice
dimensions and obtain critical values for the nonlinearity power, the
dimension, and norm density, which influence possible dynamical outcomes in a
qualitative way.Comment: 24 pages, 3 figures. arXiv admin note: text overlap with
arXiv:0901.441