Bonnemain, T., Caudrelier, V. orcid.org/0000-0003-0129-6758 and Doyon, B. (2025) Hamiltonian Formulation and Aspects of Integrability of Generalised Hydrodynamics. Annales Henri Poincaré. ISSN 1424-0637
Abstract
Generalised hydrodynamics (GHD) describes the large-scale inhomogeneous dynamics of integrable (or close to integrable) systems in one dimension of space, based on a central equation for the fluid density or quasi-particle density: the GHD equation. We consider a new, general form of the GHD equation: we allow for spatially extended interaction kernels, generalising previous constructions. We show that the GHD equation, in our general form and hence also in its conventional form, is Hamiltonian. This holds also including force terms representing inhomogeneous external potentials coupled to conserved densities. To this end, we introduce a new Poisson bracket on functionals of the fluid density, which is seen as our dynamical field variable. The total energy is the Hamiltonian whose flow under this Poisson bracket generates the GHD equation. The fluid density depends on two (real and spectral) variables, and the GHD equation can be seen as a 2 + 1-dimensional classical field theory. In its 1 + 1-dimensional reduction corresponding to the case without external forces, we further show the system admits an infinite set of conserved quantities that are in involution for our Poisson bracket, hinting at integrability of this field theory.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2025 The Author(s). This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 30 Jan 2025 14:51 |
Last Modified: | 24 Mar 2025 14:35 |
Status: | Published online |
Publisher: | Springer |
Identification Number: | 10.1007/s00023-025-01546-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:222625 |