Gaussian ensemble for quantum integrable dynamics
Files
Accepted manuscript
Date
2017-06-01
Authors
Kim, Hyungwon
Polkovnikov, Anatoli
Yuzbashyan, Emil A.
Version
OA Version
Citation
Hyungwon Kim, Anatoli Polkovnikov, Emil A Yuzbashyan. 2017. "Gaussian ensemble for quantum integrable dynamics." Annals of Physics, Volume 381, pp. 107 - 120 (14).
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.