Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons

Marcos Rigol, Vanja Dunjko, Vladimir Yurovsky, and Maxim Olshanii
Phys. Rev. Lett. 98, 050405 – Published 1 February 2007

Abstract

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)].

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  • Received 20 April 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.050405

©2007 American Physical Society

Authors & Affiliations

Marcos Rigol1, Vanja Dunjko2,3, Vladimir Yurovsky4, and Maxim Olshanii2,3,*

  • 1Physics Department, University of California, Davis, California 95616, USA
  • 2Department of Physics & Astronomy, University of Southern California, Los Angeles, California 90089, USA
  • 3Institute for Theoretical Atomic and Molecular Physics, Cambridge, Massachusetts 02138, USA
  • 4School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel

  • *Electronic address: olshanii@physics.usc.edu

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Vol. 98, Iss. 5 — 2 February 2007

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