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arXiv · 1704.03466

Solvable Hydrodynamics of Quantum Integrable Systems

Vir B. Bulchandani·Romain Vasseur·Christoph Karrasch·Joel E. Moore
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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.

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Vir B. Bulchandani, Romain Vasseur, Christoph Karrasch, Joel E. Moore. 2018-02-20. Solvable Hydrodynamics of Quantum Integrable Systems. https://doi.org/10.1103/physrevlett.119.220604

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