Ballistic space-time correlators of the classical Toda lattice

Abstract

The Toda lattice is an integrable system and its natural space-time stationary states are the generalized Gibbs ensembles (GGE). Of particular physical interest are then the space-time correlations of the conserved fields. To leading order they scale ballistically. We report on the exact solution of the respective generalized hydrodynamic equations linearized around a GGE as background state. Thereby we obtain a concise formula for the family of scaling functions.

19 pages

References in corpus (5)

• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• The collision rate ansatz for the classical Toda lattice
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• Kinetic theory of quantum and classical Toda lattices
• The GGE averaged currents of the classical Toda chain

Cited by in corpus (8)

• Diffusive Hydrodynamics of Inhomogenous Hamiltonians
• Anisotropic Landau-Lifshitz Model in Discrete Space-Time
• Dynamics of fluctuation correlation in periodically driven classical system
• Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale
• Large Deviations for Ablowitz-Ladik lattice, and the Schur flow
• High-low pressure domain wall for the classical Toda lattice
• Correlation Functions for a Chain of Short Range Oscillators
• Generalized Hydrodynamics for the Volterra lattice: Ballistic and nonballistic behavior of correlation functions