In integrable one-dimensional systems hydrodynamic noise vanishes according to a projected Kubo formula, yielding a ballistic macroscopic fluctuation theory that describes all-order hydrodynamics.
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The thermal Toda lattice is modeled as quasiparticles whose locations satisfy an asymptotic scattering relation derived from eigenvector properties of the Lax matrix.
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Hydrodynamic noise in one dimension: projected Kubo formula and how it vanishes in integrable models
In integrable one-dimensional systems hydrodynamic noise vanishes according to a projected Kubo formula, yielding a ballistic macroscopic fluctuation theory that describes all-order hydrodynamics.
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Asymptotic Scattering Relation for the Toda Lattice
The thermal Toda lattice is modeled as quasiparticles whose locations satisfy an asymptotic scattering relation derived from eigenvector properties of the Lax matrix.