Interaction quenches in the one-dimensional Bose gas

2013/05/30 by Márton Kormos, Marton Kormos, Aditya Shashi +4 · 142 citations
Mathematics · Physics and Astronomy · #Bethe ansatz #Bose gas #Bose–Einstein condensate #Canonical ensemble #Cold Atom Physics and Bose-Einstein Condensates #Conserved quantity #Integrable system #Mathematical physics #Mathematics #Non-equilibrium thermodynamics #Physics #Quadratic equation #Quantum #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #Thermalisation #cond-mat.quant-gas #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.1103/physrevb.88.205131

published in Physical Review B 88(20) (American Physical Society) · Supersedes arXiv:1204.3889. 4+ pages + Supplementary Material

arxiv created 2013/05/30 · openalex publication_date 2013/11/22 · arxiv updated 2013/11/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The nonequilibrium dynamics of integrable systems are highly constrained by the conservation of certain charges. There is substantial evidence that after a quantum quench they do not thermalize but their asymptotic steady state can be described by a generalized Gibbs ensemble (GGE) built from the conserved charges. Most of the studies on the GGE so far have focused on models that can be mapped to quadratic systems, while analytic treatment in nonquadratic systems remained elusive. We obtain results on interaction quenches in a nonquadratic continuum system, the one-dimensional (1D) Bose gas described by the integrable Lieb-Liniger model. The direct implementation of the GGE prescription is prohibited by the divergence of the conserved charges, which we conjecture to be endemic to any continuum integrable systems with contact interactions undergoing a sudden quench. We compute local correlators for a noninteracting initial state and arbitrary final interactions as well as two-point functions for quenches to the Tonks-Girardeau regime. We show that in the long time limit integrability leads to significant deviations from the predictions of the grand canonical ensemble, allowing for an experimental verification in cold-atom systems.

Citations

• Interaction quenches in the Lieb-Liniger model
• Quantum Inverse Scattering Method and Correlation Functions
• Effect of Suddenly Turning on Interactions in the Luttinger Model
• Many-body physics with ultracold gases
• Dynamics of a quantum phase transition and relaxation to a steady state
• Mode-Coupling-Induced Dissipative and Thermal Effects at Long Times after a Quantum Quench
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Finite-size corrections versus relaxation after a sudden quench

Cited by

• Exact nonequilibrium dynamics of finite-temperature Tonks-Girardeau gases
• Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium
• Quantum quench in a harmonically trapped one-dimensional Bose gas
• Quantum quenches in 1 + 1 dimensional conformal field theories
• String-charge duality in integrable lattice models
• Interplay of solitons and radiation in one-dimensional Bose gases
• Quenches from bosonic Gaussian initial states to the Tonks-Girardeau limit: Stationary states and effects of a confining potential
• Equilibration and GGE in interacting-to-free quantum quenches in dimensions d\gt 1