Theory of Nonlinear Dispersive Waves and Selection of the Ground State
arXiv:nlin/0512059 · doi:10.1103/PhysRevLett.95.213905
Abstract
A theory of time dependent nonlinear dispersive equations of the Schroedinger / Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear Master equations (NLME), governing the evolution of the mode powers, and by a novel multi-time scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include BEC large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, ``selection of the ground state'', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et. al. in nonlinear optical waveguides.
References in corpus (9)
- Resonances, Radiation Damping and Instability in Hamiltonian Nonlinear Wave Equations
- A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas
- Selection of the ground state for nonlinear Schroedinger equations
- Macroscopic Quantum Tunneling of a Bose-Einstein Condensate with Attractive Interaction
- Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods
- Stopping Light on a Defect
- Mean-field model of interaction between bright vortex solitons in Bose-Einstein condensates
- Self-Trapping, Quantum Tunneling and Decay Rates for a Bose Gas with Attractive Nonlocal Interaction
- Free expansion of attractive and repulsive Bose-Einstein condensed vortex states
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