Wave chaos in the non-equilibrium dynamics of the Gross-Pitaevskii equation
arXiv:1101.4663 · doi:10.1103/PhysRevA.83.043611
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
References in corpus (32)
- Many-Body Physics with Ultracold Gases
- Theory of Bose-Einstein condensation in trapped gases
- Chaos and Quantum Thermalization
- Anderson localization of a non-interacting Bose-Einstein condensate
- Direct observation of Anderson localization of matter-waves in a controlled disorder
- Anderson localization and nonlinearity in one dimensional disordered photonic lattices
- The cold atom Hubbard toolbox
- Dynamics of a Bright Soliton in Bose-Einstein condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential
- Destruction of Anderson localization by a weak nonlinearity
- Landau and Dynamical Instabilities of the Superflow of Bose-Einstein Condensates in Optical Lattices
- A Bose-Einstein condensate in a random potential
- Disordered quantum gases under control
- Modulational instability in cigar shaped Bose-Einstein condensates in optical lattices
- Universal spreading of wavepackets in disordered nonlinear systems
- High order symplectic integrators for perturbed Hamiltonian systems
- Suppression of Transport of an Interacting Elongated Bose-Einstein Condensate in a Random Potential
- Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
- Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
- Delocalization of a disordered bosonic system by repulsive interactions
- Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide
- Routes towards Anderson-Like localization of Bose-Einstein condensates in disordered optical lattices
- Band structure, elementary excitations, and stability of a Bose-Einstein condensate in a periodic potential
- A new class of exact solitary wave solutions of one dimensional Gross-Pitaevskii equation
- Fermi, Pasta, Ulam and a mysterious lady
- Phase Coherence and Superfluid-Insulator Transition in a Disordered Bose-Einstein Condensate
- The crossover from strong to weak chaos for nonlinear waves in disordered systems
- Anderson localization of a Bose-Einstein condensate in a 3D random potential
- Dissipative Transport of a Bose-Einstein Condensate
- Threshold for Chaos and Thermalization in One-Dimensional Mean-Field Bose-Hubbard Model
- Dipole Oscillations of a Bose-Einstein Condensate in Presence of Defects and Disorder
- Transport of ultracold Bose gases beyond the Gross-Pitaevskii description
- Inverse Scattering Transform and the Theory of Solitons
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- Effective Josephson dynamics in resonantly driven Bose-Einstein condensates
- Long-time expansion of a Bose-Einstein condensate: Can Anderson localization be observed?
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- Quench induced chaotic dynamics of Anderson localized interacting Bose-Einstein condensates in one dimension
- Beyond mean-field behavior of large Bose-Einstein condensates in double-well potentials
- Elastic scattering of a Bose-Einstein condensate at a potential landscape
- Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials
- Chaos-induced depletion of a Bose-Einstein condensate
- Conditions for order and chaos in the dynamics of a trapped Bose-Einstein condensate in coordinate and energy space
- Localization of wave packets in one-dimensional random potentials
- -coherence vs. -coherence: An alternative route to the Gross-Pitaevskii equation
- Superfluidity and collective oscillations of trapped Bose-Einstein condensates in a periodical potential
- Rabi-induced localization and resonant delocalization of a binary condensate in a spin-asymmetric quasiperiodic potential