Gaussian ensemble for quantum integrable dynamics
- Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854 (United States)
- Department of Physics, Boston University, Boston, MA 02215 (United States)
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. - Highlights: • We propose a microcanonical ensemble for the dynamics of quantum integrable systems. • The proposed ensemble is a multivariable Gaussian in the integrals of motion. • This Gaussian ensemble is exact in the classical limit at any system size. • It reproduces leading quantum corrections and finite size corrections to GGE. • The Gaussian ensemble also describes fluctuations of observables.
- OSTI ID:
- 22701501
- Journal Information:
- Annals of Physics, Vol. 381; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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