The collision rate ansatz for the classical Toda lattice

Abstract

Considered is a generalized Gibbs ensemble of the classical Toda lattice. We establish that the collision rate ansatz follows from (i) the charge-current susceptibility matrix is symmetric and (ii) the stretch current is proportional to the momentum, hence conserved.

arXiv comment9 pages, 1 figure

References in corpus (15)

• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Matrix Models for Beta Ensembles
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Kinetic equation for a dense soliton gas
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Generalised hydrodynamics of the classical Toda system
• Invariant $\beta$-ensembles and the Gauss-Wigner crossover
• Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
• Generalized Gibbs Ensembles of the classical Toda chain
• Current operators in integrable spin chains: lessons from long range deformations
• Equations of state in generalized hydrodynamics
• Collision rate ansatz for quantum integrable systems
• Kinetic theory of quantum and classical Toda lattices
• The GGE averaged currents of the classical Toda chain

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• Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography
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• Hydrodynamic Equations for the Toda Lattice
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• Anisotropic Landau-Lifshitz Model in Discrete Space-Time
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