Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap

Mario Collura, Spyros Sotiriadis, Pasquale Calabrese

Published Aug 17, 2016• 62 citations
OpenAlex

Abstract

Abstract. We consider the non-equilibrium dynamics of a gas of impenetrable bosons released from a harmonic trapping potential to a circle. The many body dynamics is solved analytically and the time dependence of all the physically relevant correlations is described. We prove that, for large times and in the thermodynamic limit, the reduced density matrix of any subsystem converges to a generalized Gibbs ensemble as a consequence of the integrability of the model. We discuss the approach to the stationary behavior at late times. We also describe the time-dependence of the entanglement entropy which attains a very simple form in the stationary state. 1.

Related papers

Quench dynamics of a Tonks–Girardeau gas released from a harmonic trap

Mario Collura, Spyros Sotiriadis, Pasquale Calabrese

We consider the non-equilibrium dynamics of a gas of impenetrable bosons released from a harmonic trapping potential to a circle. The many-body dynamics is solved analytically and the time dependence of all the physically relevant correlations is described. We prove that, for large times and in the thermodynamic limit, the reduced density matrix of any subsystem converges to a generalized Gibbs ensemble as a consequence of the integrability of the model. We discuss the approach to stationary behavior at late times. We also describe the time dependence of the entanglement entropy which attains a very simple form in the stationary state.

arXiv:1306.5604•Journal of Statistical Mechanics Theory and Experiment•Sep 30, 2013•109 citations

Equilibration of a Tonks-Girardeau Gas Following a Trap Release

Mario Collura, Spyros Sotiriadis, Pasquale Calabrese

We study the nonequilibrium dynamics of a Tonks-Girardeau gas released from a parabolic trap to a circle. We present the exact analytic solution of the many body dynamics and prove that, for large times and in a properly defined thermodynamic limit, the reduced density matrix of any finite subsystem converges to a generalized Gibbs ensemble. The equilibration mechanism is expected to be the same for all one-dimensional systems.

arXiv:1303.3795•Physical Review Letters•Jun 14, 2013•166 citations

Quench dynamics of a Tonks-Girardeau gas in one dimensional anharmonic trap

Pankaj Kumar Debnath, Barnali Chakrabarti, M. L. Lekala

Abstract The quench dynamics of strongly interacting bosons on quartic and sextic traps are studied by exactly solving the time-dependent many-boson Schrödinger equation numerically. The dynamics are addressed by the key measures of one-body density in conjugate space and information entropy. For both cases, rich many-body dynamics are exhibited and the loss of the Bose–Fermi oscillation in the Tonks–Girardeau limit is also attributed.

arXiv:2312.13532•Laser Physics Letters•Feb 12, 2024•1 citation

Quantum quench of the trap frequency in the harmonic Calogero model

M. A. Rajabpour, Spyros Sotiriadis

We consider a quantum quench of the trap frequency in a system of bosons interacting through an inverse-square potential and confined in a harmonic trap (the harmonic Calogero model). We determine exactly the initial state in terms of the postquench eigenstates and derive the time evolution of simple physical observables. Since this model possesses an infinite set of integrals of motion that allow its exact solution, a generalized Gibbs ensemble (GGE), i.e., a statistical ensemble that takes into account the conservation of all integrals of motion, can be proposed in order to describe the values of local physical observables long after the quench. Even though, due to the presence of the trap, physical observables do not exhibit equilibration but periodic evolution, such a GGE may still describe correctly their time-averaged values. We check this analytically for the local boson density and find that the GGE conjecture is indeed valid, in the thermodynamic limit.

arXiv:1307.7697•Physical Review A•Mar 14, 2014•38 citations

Quenches from bosonic Gaussian initial states to the Tonks-Girardeau limit: Stationary states and effects of a confining potential

Alvise Bastianello, Mario Collura, Spyros Sotiriadis

We consider the general problem of quenching an interacting Bose gas from the noninteracting regime to the strongly repulsive limit described by the Tonks-Girardeau gas with the initial state being a Gaussian ensemble in terms of the bosons. A generic multipoint correlation function in the steady state can be described fully in terms of a Fredholm-like determinant suitable both for a numerical and for an analytical study in certain limiting cases. Finally, we extend the study to the presence of a smooth confining potential showing that, in the thermodynamic limit, the time evolution of the two-point function can be mapped to a classical problem.

arXiv:1702.01729•Physical review. B./Physical review. B•May 23, 2017•19 citations

Dynamics of a Tonks-Girardeau gas released from a hard-wall trap

A. del Campo, Juan Gonzalo Muga

By using the Fermi-Bose map, we study the expansion dynamics of a Tonks-Girardeau gas released from a hard-wall trap. Exact analytical results are found for the density profile which differ from the density of a classical gas in the microcanonical ensemble for any observation time larger than a critical time associated with fermionization. Differences with the harmonic-trap case are discussed.

arXiv:cond-mat/0511747•Europhysics Letters (EPL)•May 16, 2006•68 citations
Abstract. We consider the non-equilibrium dynamics of a gas of impenetrable bosons released from a harmonic trapping potential to a circle. The many body dynamics is solved analytically and the time dependence of all the physically relevant correlations is described. We prove that, for large times and in the thermodynamic limit, the reduced density matrix of any subsystem converges to a generalized Gibbs ensemble as a consequence of the integrability of the model. We discuss the approach to the stationary behavior at late times. We also describe the time-dependence of the entanglement entropy which attains a very simple form in the stationary state. 1.
We consider the non-equilibrium dynamics of a gas of impenetrable bosons released from a harmonic trapping potential to a circle. The many-body dynamics is solved analytically and the time dependence of all the physically relevant correlations is described. We prove that, for large times and in the thermodynamic limit, the reduced density matrix of any subsystem converges to a generalized Gibbs ensemble as a consequence of the integrability of the model. We discuss the approach to stationary behavior at late times. We also describe the time dependence of the entanglement entropy which attains a very simple form in the stationary state.
We consider a quantum quench of the trap frequency in a system of bosons interacting through an inverse-square potential and confined in a harmonic trap (the harmonic Calogero model). We determine exactly the initial state in terms of the postquench eigenstates and derive the time evolution of simple physical observables. Since this model possesses an infinite set of integrals of motion that allow its exact solution, a generalized Gibbs ensemble (GGE), i.e., a statistical ensemble that takes into account the conservation of all integrals of motion, can be proposed in order to describe the values of local physical observables long after the quench. Even though, due to the presence of the trap, physical observables do not exhibit equilibration but periodic evolution, such a GGE may still describe correctly their time-averaged values. We check this analytically for the local boson density and find that the GGE conjecture is indeed valid, in the thermodynamic limit.
We consider the general problem of quenching an interacting Bose gas from the noninteracting regime to the strongly repulsive limit described by the Tonks-Girardeau gas with the initial state being a Gaussian ensemble in terms of the bosons. A generic multipoint correlation function in the steady state can be described fully in terms of a Fredholm-like determinant suitable both for a numerical and for an analytical study in certain limiting cases. Finally, we extend the study to the presence of a smooth confining potential showing that, in the thermodynamic limit, the time evolution of the two-point function can be mapped to a classical problem.