Solvable Hydrodynamics of Quantum Integrable Systems
Abstract
The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudo-momenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudo-momentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.
Keywords
Cite
@article{arxiv.1704.03466,
title = {Solvable Hydrodynamics of Quantum Integrable Systems},
author = {Vir B. Bulchandani and Romain Vasseur and Christoph Karrasch and Joel E. Moore},
journal= {arXiv preprint arXiv:1704.03466},
year = {2018}
}
Comments
6+5 pages, published version