Wave chaos in the non-equilibrium dynamics of the Gross-Pitaevskii equation

Abstract

The Gross-Pitaevskii equation (GPE) plays an important role in the description of Bose-Einstein condensates (BECs) at the mean-field level. The GPE belongs to the class of non-linear Schrödinger equations which are known to feature dynamical instability and collapse for attractive non-linear interactions. We show that the GPE with repulsive non-linear interactions typical for BECs features chaotic wave dynamics. We find positive Lyapunov exponents for BECs expanding in periodic and aperiodic smooth external potentials as well as disorder potentials. Our analysis demonstrates that wave chaos characterized by the exponential divergence of nearby initial wavefunctions is to be distinguished from the notion of non-integrability of non-linear wave equations. We discuss the implications of these observations for the limits of applicability of the GPE, the problem of Anderson localization, and the properties of the underlying many-body dynamics.

13 pages, 11 figures

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• Relaxation in an Extended Bosonic Josephson Junction
• Quench induced chaotic dynamics of Anderson localized interacting Bose-Einstein condensates in one dimension
• Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials
• Chaos-induced depletion of a Bose-Einstein condensate
• Rabi-induced localization and resonant delocalization of a binary condensate in a spin-asymmetric quasiperiodic potential