Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation

Abstract

We study the generalized hydrodynamics of the one-dimensional classical Non Linear Schroedinger equation in the attractive phase. We thereby show that the thermodynamic limit is entirely captured by solitonic modes and radiation is absent. Our results are derived by considering the semiclassical limit of the quantum Bose gas, where the Planck constant has a key role as a regulator of the classical soliton gas. We use our result to study adiabatic interaction changes from the repulsive to the attractive phase, observing soliton production and obtaining exact analytical results which are in excellent agreement with Monte Carlo simulations.

arXiv comment24 pages, 4 figures

References in corpus (83)

• Many-Body Physics with Ultracold Gases
• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• 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
• Time-dependence of correlation functions following a quantum quench
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Quantum Inverse Scattering Method and Correlation Functions
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Experimental Observation of a Generalized Gibbs Ensemble
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Time evolution of local observables after quenching to an integrable model
• Realization of an Excited, Strongly-Correlated Quantum Gas Phase
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Quantum dynamics of a single, mobile spin impurity
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Microscopic observation of magnon bound states and their dynamics
• Bosonizing one-dimensional cold atomic gases
• Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance
• Generalized HydroDynamics on an Atom Chip
• Hydrodynamic Diffusion in Integrable Systems
• Quasilocal charges in integrable lattice systems
• Solution for an interaction quench in the Lieb-Liniger Bose gas
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Yang-Yang thermodynamics on an atom chip
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• The Quench Action
• What is an integrable quench?
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• A note on generalized hydrodynamics: inhomogeneous fields and other concepts
• Dynamics of hard rods with initial domain wall state
• Generalized Gibbs Ensembles for Quantum Field Theories
• Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• Generalized hydrodynamics with space-time inhomogeneous interactions
• Interaction quenches in the 1D Bose gas
• Exact local correlations and full counting statistics for arbitrary states of the one-dimensional interacting Bose gas
• Superdiffusion in spin chains
• Probing three-body correlations in a quantum gas using the measurement of the third moment of density fluctuations
• Correlation functions and transport coefficients in generalised hydrodynamics
• Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions
• Correlation functions of the one-dimensional attractive Bose gas
• Extension of the Generalized Hydrodynamics to the Dimensional Crossover Regime
• Generalised hydrodynamics of the classical Toda system
• Hydrodynamics of weak integrability breaking
• Exact large-scale correlations in integrable systems out of equilibrium
• 1D Lieb-Liniger Bose Gas as Non-Relativistic Limit of the Sinh-Gordon Model
• Expectation Values in the Lieb-Liniger Bose Gas
• Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model
• Soliton gas in integrable dispersive hydrodynamics
• String-charge duality in integrable lattice models
• Superdiffusion from emergent classical solitons in quantum spin chains
• Three-body correlation functions and recombination rates for bosons in three and one dimensions
• Kardar-Parisi-Zhang universality from soft gauge modes
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• Creating quantum many-body scars through topological pumping of a 1D dipolar gas
• Algebraic construction of current operators in integrable spin chains
• Momentum-resolved study of an array of 1D strongly phase-fluctuating Bose gases
• Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
• Equilibration Properties of Classical Integrable Field Theories
• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Exact ground state of finite Bose-Einstein condensates on a ring
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Current operators in integrable models: A review
• A comparison between microscopic methods for finite temperature Bose gases
• Integrability-protected adiabatic reversibility in quantum spin chains
• Dynamics of the attractive 1D Bose gas: analytical treatment from integrability
• From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• Fragmentation and emergent integrable transport in the weakly tilted Ising chain
• Form factors and generalized hydrodynamics for integrable systems
• Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models
• Critical fluctuations in a soliton formation of attractive Bose-Einstein condensates
• Excitations of attractive 1-D bosons: Binding vs. fermionization
• Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas
• Euler-scale dynamical correlations in integrable systems with fluid motion
• On Truncated Generalized Gibbs Ensembles in the Ising Field Theory
• From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation
• Adiabatic formation of bound states in the 1d Bose gas
• The GGE averaged currents of the classical Toda chain
• The Whitham Approach to the $c\to 0$ limit of The Lieb-Liniger Model and Generalized Hydrodynamics
• Quantum corrections to the classical field approximation for one-dimensional quantum many-body systems in equilibrium
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain

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• The sine-Gordon model from coupled condensates: a Generalized Hydrodynamics viewpoint
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• Exact large-scale fluctuations of the phase field in the sine-Gordon model
• The Whitham approach to Generalized Hydrodynamics
• New classical integrable systems from generalized $T\bar{T}$-deformations
• Landau-Lifschitz magnets: exact thermodynamics and transport
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Soliton gas of the integrable Boussinesq equation and its generalised hydrodynamics
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• Particle Scattering and Fusion for the Ablowitz-Ladik Chain
• Quantum fluctuating theory for one-dimensional shock waves
• Observation of a generalized Gibbs ensemble in photonics
• Generalized Hydrodynamics for the Volterra lattice: Ballistic and nonballistic behavior of correlation functions
• Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas