Equilibration and GGE for hard wall boundary conditions

Abstract

In this work we present an analysis of a quench for the repulsive Lieb-Liniger gas confined to a large box with hard wall boundary conditions. We study the time average of local correlation functions and show that both the quench action approach and the GGE formalism are applicable for the long time average of local correlation functions. We find that the time average of the system corresponds to an eigenstate of the Lieb-Liniger Hamiltonian and that this eigenstate is related to an eigenstate of a Lieb-Liniger Hamiltonian with periodic boundary conditions on an interval of twice the length and with twice as many particles (a doubled system). We further show that local operators with support far away from the boundaries of the hard wall have the same expectation values with respect to this eigenstate as corresponding operators for the doubled system. We present an example of a quench where the gas is initially confined in several moving traps and then released into a bigger container, an approximate description of the Newton cradle experiment. We calculate the time average of various correlation functions for long times after the quench.

10 pages, 1 figure

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Cited by in corpus (19)

• Generalized Gibbs ensemble in integrable lattice models
• Quantum quenches in 1+1 dimensional conformal field theories
• The Quench Action
• Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Memory-preserving equilibration after a quantum quench in a 1d critical model
• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• The quench action approach in finite integrable spin chains
• Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering
• Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• Stationary state after a quench to the Lieb-Liniger from rotating BECs
• Dynamical depinning of a Tonks Girardeau gas
• Hydrodynamics of local excitations after an interaction quench in 1D cold atomic gases
• Entanglement prethermalization in the Tomonaga-Luttinger model
• Pulse propagation in interacting one dimensional Bose liquid
• Nonequilibrium physics in integrable systems and spin-flip non-invariant conserved quantities