We study the expansion of repulsively interacting Bose-Einstein condensates (BECs) in shallow one-dimensional potentials. We show for these systems that the onset of wave chaos in the Gross-Pitaevskii equation (GPE), i.e. the onset of exponential separation in Hilbert space of two nearby condensate wave functions, can be used as indication for the onset of depletion of the BEC and the occupation of excited modes within a many-body description. Comparison between the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method and the GPE reveals a close correspondence between the many-body effect of depletion and the mean-field effect of wave chaos for a wide range of single-particle external potentials. In the regime of wave chaos the GPE fails to account for the fine-scale quantum fluctuations because many-body effects beyond the validity of the GPE are non-negligible. Surprisingly, despite the failure of the GPE to account for the depletion, coarse grained expectation values of the single-particle density such as the overall width of the atomic cloud agree very well with the many-body simulations. The time dependent depletion of the condensate could be investigated experimentally, e.g., via decay of coherence of the expanding atom cloud.
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