Recurrence time in the quantum dynamics of the 1D Bose gas

Kaminishi, Eriko; Sato, Jun; Deguchi, Tetsuo

doi:10.48550/arxiv.1305.3412

Cited by 7 publications

(12 citation statements)

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“…However, to date, the construction of a quantum state with the degree of correlation necessary to evolve like a soliton has been challenging. In fact, different attempts to superimpose excited states to generate stable localized excitations have generated unstable configurations which in time lose coherence and fall apart [37,38]. This failure of theoretical attempts indicates that some clever insight is needed to generate a quantum state that propagates without changing its macroscopic properties, while such configurations are easily produced in the laboratories as a results of certain non-equilibrium dynamics.…”

mentioning

confidence: 99%

Universal dynamics of a soliton after an interaction quench

Franchini

Gromov

Kulkarni

et al. 2015

J. Phys. A: Math. Theor.

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We propose a new type of experimentally feasible quantum quench protocol in which a quantum system is prepared in a coherent, localized excited state of a Hamiltonian. During the evolution of this solitonic excitation, the microscopic interaction is suddenly changed. We study the dynamics of solitons after this interaction quench for a wide class of systems using a hydrodynamic approach. We find that the post-quench dynamics is universal at short times, i.e. it does not depend on the microscopic details of the physical system. Numerical support for these results is presented using generalized non-linear Schrödinger equation, relevant for the implementation of the proposed protocol with ultracold bosons, as well as for the integrable Calogero model in harmonic potential. Finally, it is shown that the effects of integrability breaking by a parabolic potential and by a power-law non-linearity do not change the universality of the short-time dynamics.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45.Yv, 05.70.Ln, 02.30.Ik Recent years have witnessed a rising interest in nonequilibrium dynamics, which has been largely motivated by extraordinary progresses in the manipulation of manybody quantum systems [1][2][3][4][5][6][7][8][9][10][11][12]. This interplay between experimental and theoretical research is allowing the investigation of longstanding questions, such as under which conditions systems driven out of equilibrium can show universal behaviors and whether and how a system reaches equilibrium and possibly thermalizes [13][14][15][16][17][18][19][20][21][22][23], in particular in cold atom systems [24][25][26][27][28].A particularly interesting protocol used to identify paradigms of out-of-equilibrium dynamics is provided by the quantum quenches, in which, typically, a system described by a Hamiltonian H is prepared in its ground state and then, at a given moment of time, let evolved using a different Hamiltonian H [29]. Although a unitary evolution cannot relax the system to a true equilibrium, mounting evidences support a picture for which, in most cases, the expectation value of most local operators tending to a stationary value in the long time limit can be calculated through an effective density matrix describing the system [15][16][17][30][31][32][33][34][35][36]: that is, an arbitrary out-ofequilibrium many-body state in general evolves toward a state that effectively cannot be distinguished from a mixed state.In this work, inspired by these progresses and motivated by experimental considerations, we propose a new protocol based on a quench of the interaction on an inhomogeneous initial state localized in space: this protocol has the merit of showing universal dynamics already at short times after the quench, while to date most of the studies on universal effects in quantum quenches focus on long times. We focus in particular on one-dimensional (1d) systems, where localized solitonic states are present and stable in a variety of models, even though we expect that our results are valid in any dimension provided ...

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confidence: 99%

Universal dynamics of a soliton after an interaction quench

Franchini

Gromov

Kulkarni

et al. 2015

J. Phys. A: Math. Theor.

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“…For the small number of particles such as N = 20, we observed recurrence phenomenon [50]. In particular, in the free-fermionic and the free-bosonic regimes, there are many quantum states which show recurrence [57].…”

Section: Recurrence Of the Density Notchmentioning

confidence: 84%

Exact quantum dynamics of yrast states in the finite 1D Bose gas

Kaminishi

Sato

Deguchi

2014

J. Phys.: Conf. Ser.

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We demonstrate that the quantum dynamics of yrast states in the one-dimensional (1D) Bose gas gives an illustrative example to equilibration of an isolated quantum many-body system. We first formulate the energy spectrum of yrast states in terms of the dressed energy by applying the method of finite-size corrections. We then review the exact time evolution of quantum states constructed from yrast states shown by the Bethe ansatz. In time evolution the density profile of an initially localized quantum state constructed from yrast states collapses into a flat profile in the case of a large particle number such as N = 1000, while recurrence of the localized state occurs in the case of a small particle number such as N = 20. We suggest that the dynamical relaxation behavior for the large N case is consistent with the viewpoint of typicality for generic quantum states: the expectation values of local operators evaluated in most of quantum states are very close to those of the micro-canonical ensemble.

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“…For much longer times, boundaries start to be relevant in the dynamics and a complete timereversal symmetric state is restored, where all the expectation values of local operators coincide with the mean between their thermal average in the two disconnected chains. This regime can be observed for T T rev , where T rev ∝ L 2 is the typical revival time of a free fermionic chain 12,22 . As expected, thermalization occurs in a Generalized Gibbs Ensemble (GGE).…”

Section: Introductionmentioning

confidence: 88%

“…2 prefactor as an inessential constant term inside S Q . Notice that since Ô is a local operator the matrix element N Φ| Ô|Φ N is a smooth function of the set of momenta {φ } that can be replaced for our purposes by a functional h[ρ ] appearing in (22). The reason is that local observables can only affect microscopic details of the densities ρ , ρ, which result in sub-leading contributions in the thermodynamic limit.…”

Section: The Quench Actionmentioning

confidence: 99%

Stationary states in a free fermionic chain from the quench action method

2015

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We employ the Quench Action Method (QAM) for a recently considered geometrical quantum quench: two free fermionic chains initially at different temperatures are joined together in the middle and let evolve unitarily with a translation invariant Hamiltonian. We show that two different stationary regimes are reached at long times, depending on the interplay between the observation time scale T and the total length L of the system. We show the emergence of a non-equilibrium steady state (NESS) supporting an energy current for observation time T much smaller than the system size L. We then identify a longer time-scale for which thermalization occurs in a Generalized Gibbs Ensemble (GGE).

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Recurrence time in the quantum dynamics of the 1D Bose gas

Cited by 7 publications

References 0 publications

Universal dynamics of a soliton after an interaction quench

Universal dynamics of a soliton after an interaction quench

Exact quantum dynamics of yrast states in the finite 1D Bose gas

Stationary states in a free fermionic chain from the quench action method

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