A geometric viewpoint on generalized hydrodynamics
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2018-01-01
|
| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321317303875 |
| _version_ | 1818692210713952256 |
|---|---|
| author | Benjamin Doyon Herbert Spohn Takato Yoshimura |
| author_facet | Benjamin Doyon Herbert Spohn Takato Yoshimura |
| author_sort | Benjamin Doyon |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T12:54:10Z |
| format | Article |
| id | doaj.art-40f939ca969043bbad3d2528a8b88ba8 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-12-17T12:54:10Z |
| publishDate | 2018-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-40f939ca969043bbad3d2528a8b88ba82022-12-21T21:47:31ZengElsevierNuclear Physics B0550-32131873-15622018-01-01926C57058310.1016/j.nuclphysb.2017.12.002A geometric viewpoint on generalized hydrodynamicsBenjamin Doyon0Herbert Spohn1Takato Yoshimura2Department of Mathematics, King's College London, Strand, London WC2R 2LS, UKPhysik Department and Zentrum Mathematik, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, GermanyDepartment of Mathematics, King's College London, Strand, London WC2R 2LS, UKGeneralized 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.http://www.sciencedirect.com/science/article/pii/S0550321317303875 |
| spellingShingle | Benjamin Doyon Herbert Spohn Takato Yoshimura A geometric viewpoint on generalized hydrodynamics Nuclear Physics B |
| title | A geometric viewpoint on generalized hydrodynamics |
| title_full | A geometric viewpoint on generalized hydrodynamics |
| title_fullStr | A geometric viewpoint on generalized hydrodynamics |
| title_full_unstemmed | A geometric viewpoint on generalized hydrodynamics |
| title_short | A geometric viewpoint on generalized hydrodynamics |
| title_sort | geometric viewpoint on generalized hydrodynamics |
| url | http://www.sciencedirect.com/science/article/pii/S0550321317303875 |
| work_keys_str_mv | AT benjamindoyon ageometricviewpointongeneralizedhydrodynamics AT herbertspohn ageometricviewpointongeneralizedhydrodynamics AT takatoyoshimura ageometricviewpointongeneralizedhydrodynamics AT benjamindoyon geometricviewpointongeneralizedhydrodynamics AT herbertspohn geometricviewpointongeneralizedhydrodynamics AT takatoyoshimura geometricviewpointongeneralizedhydrodynamics |