Thibault Bonnemain

Jeudi 20 Mars 2025, 14h00, salle E4.13b

Thibault BONNEMAIN

PhLAM, Université de Lille

Hamiltonian formulation and aspects of integrability of generalised Hydrodynamics

Generalised Hydrodynamics (GHD) describes the large-scale inhomogeneous dynamics of integrable (or close to integrable) systems in one dimension of space via an autonomous hydrodynamic equation. In this talk, I will present a general form of the GHD equation, notably allowing for integrability-breaking perturbations and spatially extended interaction kernels, and show that it constitutes an Hamiltonian system. To this end, I will introduce a Poisson bracket on functionals of the fluid (or quasi-particle) density, which is seen as our dynamical field variable.The fluid density depends on two (spatial and spectral) variables so that, contrary to the underlying microscopic system which which gives rise to GHD at large scales, the GHD equation can be seen as a (2 +1)-dimensional classical field theory. The total energy of the underlying model is the Hamiltonian whose flow, under this Poisson

bracket, generates the GHD equation. Furthermore, the system admits an infinite set of conserved quantities that are in involution for our Poisson bracket, hinting at integrability of this field theory.

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