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arXiv:1806.09343 · Physical Review A

Quantum quench and thermalization of one-dimensional Fermi gas via phase-space hydrodynamics

Manas Kulkarni, Goutam Mandal, Takeshi Morita

Published Oct 8, 2018• 26 citations
arXivHTMLPDF

Abstract

By exploring a phase-space hydrodynamics description of one-dimensional free Fermi gas, we discuss how systems settle down to steady states described by the generalized Gibbs ensembles through quantum quenches. We investigate time evolutions of the fermions which are trapped in external potentials or a circle for a variety of initial conditions and quench protocols. We analytically compute local observables such as particle density and show that they always exhibit power-law relaxation at late times. We find a simple rule which determines the power law exponent. Our findings are, in principle, observable in experiments in a one-dimensional free Fermi gas or Tonk's gas (Bose gas with infinite repulsion).

DOI
10.1103/physreva.98.043610

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By exploring a phase-space hydrodynamics description of one-dimensional free Fermi gas, we discuss how systems settle down to steady states described by the generalized Gibbs ensembles through quantum quenches. We investigate time evolutions of the fermions which are trapped in external potentials or a circle for a variety of initial conditions and quench protocols. We analytically compute local observables such as particle density and show that they always exhibit power-law relaxation at late times. We find a simple rule which determines the power law exponent. Our findings are, in principle, observable in experiments in a one-dimensional free Fermi gas or Tonk's gas (Bose gas with infinite repulsion).
We consider a quantum quench in a noninteracting fermionic one-dimensional field theory. The system of size LLL is initially prepared into two halves L\mathcal{L}L $([\ensuremath{-}L/2,0])$ and R\mathcal{R}R ([0,L/2])([0,L/2])([0,L/2]), each of them thermalized at two different temperatures TL{T}_{\mathcal{L}}TL​ and TR{T}_{\mathcal{R}}TR​, respectively. At a given time, the two halves are joined together by a local coupling and the whole system is left to evolve unitarily. For an infinitely extended system $(L\ensuremath{\rightarrow}\ensuremath{\infty})$, we show that the time evolution of the particle and energy densities is well described via a hydrodynamic approach which allows us to evaluate the correspondent stationary currents. We show, in such a case, that the two-point correlation functions are deduced, at large times, from a simple nonequilibrium steady state. Otherwise, whenever the boundary conditions are retained (in a properly defined thermodynamic limit), any current is suppressed at large times, and the stationary state is described by a generalized Gibbs ensemble, which is diagonal and depends only on the post-quench mode occupation.
Abstract We study the relaxation dynamics and statistical properties of hard-core bosons in a one-dimensional quasiperiodic lattice with a power-law potential following a quantum quench. Through numerical simulation of the time evolution of various one-body observables, including the on-site density, the momentum distribution, and natural orbital occupations, we find that these observables relax to non-thermal steady states. The temporal fluctuations around these steady values vanish in the thermodynamic limit. Moreover, the long-time statistics of all observables are precisely captured by a generalized Gibbs ensemble. This result confirms that generalized thermalization remains valid even in systems featuring mobility edges, where extended and localized single-particle states coexist. Our findings offer a quantitative basis for future experiments on generalized thermalization using quantum simulators with tunable mobility edges.
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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.
In the present thesis we study the unitary dynamics and the thermalization properties of free-fermion-like Hamiltonians after a sudden quantum quench in presence of disorder. With analytical and numerical arguments, we show that the existence of a stationary state and its description with a generalized Gibbs ensemble (GGE) depend crucially on the observable considered (local versus extensive, one-body versus many-body) and on the localization properties of the final Hamiltonian. We then show an extension of the Wang-Landau algorithm which allows the computation of weighted distributions associated to quantum quenches, like the diagonal and the GGE ensemble expectation-value distributions. We present results on three one-dimensional models, the Anderson model, a disordered one-dimensional fermionic chain with long-range hopping, and the disordered Ising/XY spin chain.
We investigate the nonequilibrium evolution of density correlations in a thermal one-dimensional Bose gas following a trap quench. We focus on the Tonks--Girardeau limit and develop an analytical description based on a finite-temperature extension of Quantum Generalized Hydrodynamics. We benchmark our predictions against exact numerics for a quench from a double well to a harmonic trap and for a trap release, and assess their temperature range of validity. Our results capture the dynamical enhancement of correlations during the expansion stages, namely the crossover from thermally suppressed to power-law bulk correlations. For the trap release, the conformal distance associated with fixed bulk points decreases as 1/t1/t1/t, so the correlations progressively probe a universal regime~∼1/x2\sim1/x^2∼1/x2 that is independent of temperature. We thus show that, in the hydrodynamic long-time regime, the bulk density correlations approach their zero-temperature equilibrium form independently of the initial temperature.