Research output: Contribution to journal › Article

Benjamin Doyon, Herbert Spohn, Takato Yoshimura

Original language | English |
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Pages (from-to) | 570-583 |

Journal | Nuclear Physics, Section B |

Volume | 926 |

Early online date | 6 Dec 2017 |

DOIs | |

State | E-pub ahead of print - 6 Dec 2017 |

**A geometric viewpoint on_DOYON_Publishedonline6December2017_GOLD CP (CC BY)**A_geometric_viewpoint_on_DOYON_Publishedonline6December2017_GOLD_VoR_CC_BY_.pdf, 661 KB, application/pdf

7/12/2017

Proof

CC BY

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.

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