Statistical mechanics of a nonlinear discrete system

Abstract

Statistical mechanics of the discrete nonlinear Schrödinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of $T=\infty$, we identify a phase transition, through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breather-like localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.

4 pages, 3 figures

Cited by in corpus (92)

• Topological Photonics
• Topological Photonics
• The physics of dipolar bosonic quantum gases
• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• Thermodynamic theory of highly multimoded nonlinear optical systems
• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• Non-ergodic metallic and insulating phases of Josephson junction chains
• Intermittent many-body dynamics at equilibrium
• Radiationless Travelling Waves In Saturable Nonlinear Schrödinger Lattices
• A simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities
• One-Dimensional Optical Wave Turbulence: Experiment and Theory
• Optical wave turbulence and condensation of light
• Standing wave instabilities in a chain of nonlinear coupled oscillators
• Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
• Negative Temperature States in the Discrete Nonlinear Schroedinger Equation
• The nonequilibrium discrete nonlinear Schroedinger equation
• Statistical mechanics of general discrete nonlinear Schr{ö}dinger models: Localization transition and its relevance for Klein-Gordon lattices
• The Discrete Nonlinear Schrödinger equation - 20 Years on
• Statistical Mechanics of Systems with Negative Temperature
• Condensation transition in the late-time position of a Run-and-Tumble particle
• Localization and Coherence in Nonintegrable Systems
• Optical Phase Transitions in Photonic Networks: A Spin System Formulation
• Free-energy transition in a gas of non-interacting nonlinear wave-particles
• Dynamical freezing of relaxation to equilibrium
• Localization transition in the Discrete Non-Linear Schrödinger Equation: ensembles inequivalence and negative temperatures
• Dynamical glass in weakly non-integrable Klein-Gordon chains
• Off-equilibrium Langevin dynamics of the discrete nonlinear Schroedinger chain
• Discrete breathers in thermal equilibrium: distributions and energy gaps
• Self-Trapping of Bose-Einstein Condensates in an Optical Lattice: the Effect of the System Dimension
• Universal Correlations and Dynamic Disorder in a Nonlinear Periodic 1D System
• Anomalous scaling and first-order dynamical phase transition in large deviations of the Ornstein-Uhlenbeck process
• Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation
• Skin modes in a nonlinear Hatano-Nelson model
• Condensation transition in joint large deviations of linear statistics
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• A Chain, a Bath, a Sink and a Wall
• Coarsening dynamics in a simplified DNLS model
• Condensation transition and ensemble inequivalence in the Discrete Nonlinear Schrödinger Equation
• Phase transitions at high energy vindicate negative microcanonical temperature
• Controlling Optical Beam Thermalization via Band-Gap Engineering
• Coupled transport in rotor models
• Chaos and localization in the Discrete Nonlinear Schrödinger Equation
• Statistical physics of nonlinear wave interaction
• The nature of self-localization of Bose-Einstein condensates in deep optical lattices
• Thermalization of Strongly Disordered Nonlinear Chains
• Relaxation and coarsening of weakly-interacting breathers in a simplified DNLS chain
• Fundamental entropic processes in the theory of optical thermodynamics
• Modulational instability in isolated and driven Fermi--Pasta--Ulam lattices
• Boundary-induced instabilities in coupled oscillators
• Non-Gibbs states on a Bose-Hubbard lattice
• Decay of DNLS breathers through inelastic multiphonon scattering
• Finite-size localization scenarios in condensation transitions
• Fragile Many Body Ergodicity
• Statistical Mechanics of a Discrete Schrödinger Equation with Saturable Nonlinearity
• Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices
• Spreading, Nonergodicity, and Selftrapping: a puzzle of interacting disordered lattice waves
• Negative temperature states as exact equilibrium solutions of the Wave Kinetic equation for one dimensional lattices
• Density Resolved Wave Packet Spreading in Disordered Gross-Pitaevskii Lattices
• Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization
• Entropy production for complex Langevin equations
• Localization in the Discrete Non-Linear Schrödinger Equation and geometric properties of the microcanonical surface
• Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
• Thermalized polarization dynamics of a discrete optical waveguide system with four-wave mixing
• Condensation induced by coupled transport processes
• Thermalization in the one-dimensional Salerno model lattice
• Coupled transport in a linear-stochastic Schrödinger Equation
• Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonian
• Gauge invariance and geometric phase in nonequilibrium thermodynamics
• Quench dynamics in disordered two-dimensional Gross-Pitaevskii Lattices
• Intensity pseudo-localized phase in the glassy random laser
• Dynamical regimes of finite temperature discrete nonlinear Schrödinger chain
• H-theorem at negative temperature: the random exchange model with bounds
• Localization in boundary-driven lattice models
• Anderson localization of excitations in disordered Gross-Pitaevskii lattices
• Statistical analysis of complex systems with nonclassical invariant measures
• Statistics of noise-driven coupled nonlinear oscillators: applications to systems with Kerr nonlinearity
• Mobility edges and fractal states in quasiperiodic Gross-Pitaevskii chains
• Onsager coefficients in a coupled-transport model displaying a condensation transition
• Standing and Traveling Waves in a Nonlinearly Dispersive Lattice Model
• Thermal lifetime of breathers
• Relaxation dynamics and finite-size effects in a simple model of condensation
• Efficient numerical evaluation of thermodynamic quantities on infinite (semi-)classical chains
• Thermalization in a nonlinear variant of the discrete nonlinear Schrödinger Equation
• Infinite-temperature thermostats by energy localization in a nonequilibrium setup
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems
• Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation
• Frozen dynamics of a breather induced by an adiabatic invariant
• First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization
• Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions
• Diffusive limit and Fourier's law for the discrete Schroedinger equation