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Journal of Modern Optics

(Quantum) chaos in Bose-Einstein condensates

S. A. Gardiner

Published Oct 1, 2002• 14 citations
Publisher

Abstract

I discuss chaos in classical and quantum (wave) dynamics, extending this to considering chaotic dynamics in nonlinear wave equations, in particular how chaotic dynamics in the Gross-Pitaevskii equation relate to particle depletion from an initial Bose-Einstein condensate.
DOI
10.1080/09500340210140777

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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 nonlinear Schr\"odinger equations which are known to feature dynamical instability and collapse for attractive nonlinear interactions. We show that the GPE with repulsive nonlinear 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 wave functions is to be distinguished from the notion of nonintegrability of nonlinear 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.