A geometric viewpoint on generalized hydrodynamics

Doyon, Benjamin (Department of Mathematics, King's College London, Strand, London, WC2R 2LS, UK) ; Spohn, Herbert (Physik Department and Zentrum Mathematik, Technische Universität München, Boltzmannstrasse 3, Garching, 85748, Germany) ; Yoshimura, Takato (Department of Mathematics, King's College London, Strand, London, WC2R 2LS, UK)

05 December 2017

Abstract: Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective (“dressed”) velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles; in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.

Published in: Nuclear Physics B (2017)
Published by: Elsevier
DOI: 10.1016/j.nuclphysb.2017.12.002
License: CC-BY-3.0

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