Wave chaos in the nonequilibrium dynamics of the Gross-Pitaevskii equation

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.043611· OSTI ID:21544672

Brezinova, Iva; Ludwig, Katharina; Burgdoerfer, Joachim ^[1]; Collins, Lee A ^[2]; Schneider, Barry I ^[3]

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1. Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria)
2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
3. Physics Division, National Science Foundation, Arlington, Virginia 22230 (United States)

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 Schroedinger 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.

• OSTI ID: 21544672
• Journal Information: Physical Review. A, Vol. 83, Issue 4; Other Information: DOI: 10.1103/PhysRevA.83.043611; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
BOSE-EINSTEIN CONDENSATION
CHAOS THEORY
INSTABILITY
INTERACTIONS
LYAPUNOV METHOD
MANY-BODY PROBLEM
MEAN-FIELD THEORY
NONLINEAR PROBLEMS
POTENTIALS
SCHROEDINGER EQUATION
WAVE FUNCTIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS