Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials
arXiv:2304.10308 · doi:10.1103/PhysRevE.108.034204
Abstract
We identify a class of trapping potentials in cubic nonlinear Schrödinger equations (NLSEs) that make them non-integrable, but prevent the emergence of power spectra associated with ergodicity. The potentials are characterized by equidistant energy spectra (e.g., the harmonic-oscillator trap), which give rise to a large number of resonances enhancing the nonlinearity. In a broad range of dynamical solutions, spanning the regimes in which the nonlinearity may be either weak or strong in comparison with the linear part of the NLSE, the power spectra are shaped as narrow (quasi-discrete) evenly spaced spikes, unlike generic truly continuous (ergodic) spectra. We develop an analytical explanation for the emergence of these spectral features in the case of weak nonlinearity. In the strongly nonlinear regime, the presence of such structures is tracked numerically by performing simulations with random initial conditions. Some potentials that prevent ergodicity in this manner are of direct relevance to Bose-Einstein condensates: they naturally appear in 1D, 2D and 3D Gross-Pitaevskii equations (GPEs), the quintic version of these equations, and a two-component GPE system.
arXiv commentaccepted for publication in Phys. Rev. E: https://journals.aps.org/pre/accepted/09078R97Q4416e2c54e76e7865eca7be213aa2a50
References in corpus (72)
- Theory of Bose-Einstein condensation in trapped gases
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Dark Solitons in Bose-Einstein Condensates
- Relaxation and Pre-thermalization in an Isolated Quantum System
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture
- Generalized Gibbs ensemble in integrable lattice models
- Experimental Observation of a Generalized Gibbs Ensemble
- Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
- Emergent hydrodynamics in integrable quantum systems out of equilibrium
- Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
- Evolution of a Bose-condensed gas under variations of the confining potential
- Motion of dark solitons in trapped Bose-Einstein condensates
- Ultracold atoms out of equilibrium
- Experimental observation of oscillating and interacting matter wave dark solitons
- Breathing Modes and Hidden Symmetry of Trapped Atoms in 2D
- Thermalization near integrability in a dipolar quantum Newton's cradle
- Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate
- Optical Rogue Waves in integrable turbulence
- Generalized hydrodynamics in strongly interacting 1D Bose gases
- Gap-Townes solitons and localized excitations in low dimensional Bose Einstein condensates in optical lattices
- Integrable turbulence and formation of rogue waves
- Soliton creation during a Bose-Einstein condensation
- One-Dimensional Quasi-Exactly Solvable Schrödinger Equations
- Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
- Rayleigh-Jeans condensation of classical light : Observation and thermodynamic characterization
- Statistical mechanics of beam self-cleaning in GRIN multimode optical fibers
- Dynamics of Collapse of a Confined Bose Gas
- Extension of the Generalized Hydrodynamics to the Dimensional Crossover Regime
- Thermalization and pseudolocality in extended quantum systems
- Dramatic acceleration of wave condensation mediated by disorder in multimode fibers
- Thermalisation of a trapped one-dimensional Bose gas via diffusion
- Strongly interacting soliton gas and formation of rogue waves
- Soliton-sound interactions in quasi-one-dimensional Bose-Einstein condensates
- Self-organization in nonlinear wave turbulence
- Prethermalization Revealed by the Relaxation Dynamics of Full Distribution Functions
- Incomplete thermalization from trap-induced integrability breaking: lessons from classical hard rods
- Thermodynamics of an interacting trapped Bose-Einstein gas in the classical field approximation
- Dynamics of two interacting Bose-Einstein condensates
- Nonlinear random optical waves: integrable turbulence, rogue waves and intermittency
- A comparison between microscopic methods for finite temperature Bose gases
- Wave chaos as signature for depletion of a Bose-Einstein condensate
- Observation of light thermalization to negative temperature Rayleigh-Jeans equilibrium states in multimode optical fibers
- Bright Solitary-Matter-Wave Collisions in a Harmonic Trap: Regimes of Soliton-like Behaviour
- Interference of a Bose-Einstein condensate in a hard-wall trap: Formation of vorticity
- Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates
- Dynamical instability of a dark soliton in a quasi-one-dimensional Bose-Einstein condensate perturbed by an optical lattice
- Wave chaos in the non-equilibrium dynamics of the Gross-Pitaevskii equation
- Dark soliton decay due to trap anharmonicity in atomic Bose-Einstein condensates
- On the Cubic Lowest Landau Level Equation
- Delayed collapses of BECs in relation to AdS gravity
- Ultraviolet asymptotics and singular dynamics of AdS perturbations
- Thermalization in a one-dimensional integrable system
- Dissociation of one-dimensional matter-wave breathers due to quantum many-body effects
- Thermalization of a quantum Newton's cradle in a one-dimensional quasicondensate
- Probing quasi-integrability of the Gross-Pitaevskii equation in a harmonic-oscillator potential
- Two infinite families of resonant solutions for the Gross-Pitaevskii equation
- Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes
- Quantitative study of quasi-one-dimensional Bose gas experiments via the stochastic Gross-Pitaevskii equation
- Solvable cubic resonant systems
- Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations
- Integrable turbulence developing from strongly nonlinear partially coherent waves
- Long-time expansion of a Bose-Einstein condensate: Can Anderson localization be observed?
- A nonrelativistic limit for AdS perturbations
- Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss
- Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap
- Complex plane representations and stationary states in cubic and quintic resonant systems
- Rayleigh-Jeans thermalization vs beam cleaning in multimode optical fibers
- Dynamics and thermalization of Bose-Einstein condensate in Sinai oscillator trap
- Breathing modes, quartic nonlinearities and effective resonant systems
- Comparison of Split-Step and Hamiltonian Integration Methods for Simulation of the Nonlinear Schrödinger Equation
- Trapping wave fields in an expulsive potential by means of linear coupling