Disordered Bose Einstein Condensates with Interaction in One Dimension

Abstract

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.

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• Multiparticle localization for disordered systems on continuous space via the fractional moment method
• Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas
• Superfluid behavior of a Bose-Einstein condensate in a random potential
• Finite Temperature Off-Diagonal Long-Range Order for Interacting Bosons
• Bose--Einstein condensation in the Luttinger--Sy model with contact interaction
• Instability of Bose-Einstein condensation on quantum graphs under repulsive perturbations
• On a condition for type-I Bose-Einstein condensation in random potentials in $d$ dimensions
• Localization landscape for interacting Bose gases in one-dimensional speckle potentials
• Ground State Energy of Mean-field Model of Interacting Bosons in Bernoulli Potential
• Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential
• On Bose-Einstein condensation in interacting Bose gases in the Kac-Luttinger model