Interaction quench in a trapped one-dimensional Bose gas

Abstract

We study the non-equilibrium quench dynamics from free to hard-core one-dimensional bosons in the presence of a hard-wall confining potential. We characterise the density profile and the two-point fermionic correlation function in the stationary state as well as their full time evolution. We find that for long times the system relaxes to a uniform density profile, but the correlation function keeps memory of the initial state with a stationary algebraic long-distance decay as opposite to the exponential behaviour found for the same quench in the periodic setup. We also compute the stationary bosonic two-point correlator which turns out to decay exponentially for large distances. We show that a two-step mechanism governs the time evolution: a quick approach to an almost stationary value is followed by a slow algebraic relaxation to the true stationary state.

23 pages, 8 figures

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• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Pre-relaxation in weakly interacting models
• Exact solution for the quench dynamics of a nested integrable system
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
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• Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• One-dimensional Bose gas driven by a slow time-dependent harmonic trap