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 state are. We confirm the relaxation hypothesis through a thorough 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 having already been observed in the recent experiment on the non-equilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita, T. Wenger, D. S. Weiss, Nature (London) 440, 900 (2006)].
We study the system of coupled atomic and molecular condensates within the two-mode model and beyond mean-field theory (MFT). Large amplitude atom-molecule coherent oscillations are shown to be damped by the rapid growth of fluctuations near the dynamically unstable molecular mode. This result contradicts earlier predictions about the recovery of atom-molecule oscillations in the two-mode limit. The frequency of the damped oscillation is also shown to scale as √ N / log N with the total number of atoms N , rather than the expected pure √ N scaling. Using a linearized model, we obtain analytical expressions for the initial depletion of the molecular condensate in the vicinity of the instability, and show that the important effect neglected by mean field theory is an initially non-exponential 'spontaneous' dissociation into the atomic vacuum. Starting with a small population in the atomic mode, the initial dissociation rate is sensitive to the exact atomic amplitudes, with the fastest (super-exponential) rate observed for the entangled state, formed by spontaneous dissociation.Recent photoassociation [1] and Feshbach resonance [2,3] experiments suggest the possibility of producing molecular Bose-Einstein condensates (BEC) [4][5][6][7][8][9]. Large amplitude coherent oscillations between an atomic BEC and a molecular BEC have been theoretically predicted [4][5][6]. A common theme to these studies is the use of the Gross-Pitaevskii (GP) mean-field theory (MFT), reducing the full multi-body problem into a set of two coupled nonlinear Schrödinger equations. These are then solved numerically to obtain the Josephson-type dynamics of the coupled atomic and molecular fields.The simple GP dynamics is substantially affected by condensate depletion due to inelastic collisions [5,7,10], spontaneous emission, and the inclusion of noncondensate modes [10][11][12][13][14]. Consequently, the atommolecule oscillations are expected to be strongly damped under current experimental conditions. The proposed remedy for this detrimental effect involves a recovery of an effective two-mode dynamics [13], thereby preventing the buildup of thermal population.In this article we point out that even in the perfect twomode limit, MFT fails to provide long-term predictions due to strong interparticle entanglement near the dynamically unstable molecular mode. Quantum corrections to MFT appear in the vicinity of its dynamical instabilities, on time scales that grow only logarithmically with the number N of condensate particles [15][16][17]. Thus, even in the absence of a 'proper' thermal bath of noncondensate states, the mean-field equations are coupled to a reservoir of Bogoliubov fluctuations [16,18]. The rapid growth of these fluctuations near the instability is analogous to the rapid population of the thermal cloud, similarly inhibiting the mean-field atom-molecule oscillations. Our results, obtained using the numerical solution of exact quantum equations, go beyond the HartreeFock-Bogoliubov approach [12]. The leading quantum effect is identi...
In recent experiments on Na Bose-Einstein condensates [S. Inouye et al, Nature 392, 151 (1998); J. Stenger et al, Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of pairs of atoms belonging to the condensate many-body wavefunction. A mechanism is offered here to account for the observed losses, based on the deactivation of the resonant molecular state by interaction with a third condensate atom.Comment: LaTeX, 4 pages, 4 PostScript figures, uses REVTeX and psfig, submitted to Physical Review A, Rapid Communication
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