Scholarlink

<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>-dimensional classical field theory. In its <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>-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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Hamiltonian Formulation and Aspects of Integrability of Generalised Hydrodynamics

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年3月3日

查看全文
  • Thibault Bonnemain,
  • Vincent Caudrelier,
  • Benjamin Doyon

摘要

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 \(2+1\) 2 + 1 -dimensional classical field theory. In its \(1+1\) 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.