Gaussian ensemble for quantum integrable dynamics
arXiv:1606.08459 · doi:10.1016/j.aop.2017.03.022
Abstract
We propose a Gaussian ensemble as a description of the long-time dynamics of isolated quantum integrable systems. Our approach extends the Generalized Gibbs Ensemble (GGE) by incorporating fluctuations of integrals of motion. It is asymptotically exact in the classical limit irrespective of the system size and, under appropriate conditions, in the thermodynamic limit irrespective of the value of Planck's constant. Moreover, it captures quantum corrections near the classical limit, finite size corrections near the thermodynamic limit, and is valid in the presence of non-local interactions. The Gaussian ensemble bridges the gap between classical integrable systems, where a generalized microcanonical ensemble is exact even for few degrees of freedom and GGE, which requires thermodynamic limit. We illustrate our results with examples of increasing complexity.
10 pages, 4 figures
References in corpus (7)
- Non-equilibrium coherence dynamics in one-dimensional Bose gases
- Experimental Observation of a Generalized Gibbs Ensemble
- Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
- Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
- Quantum quench phase diagrams of an s-wave BCS-BEC condensate
- Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
- Measuring effective temperatures in a generalized Gibbs ensemble