Equilibrium dynamical correlations in the Toda chain and other integrable models

Abstract

We investigate the form of equilibrium spatio-temporal correlation functions of conserved quantities, and of energy transport in the Toda lattice and in other integrable models. From numerical simulations we find that the correlations satisfy ballistic scaling with a remarkable collapse of data from different times. We examine special limiting choices of parameter values, for which the Toda lattice tends to either the harmonic chain or the equal mass hard-particle gas. In both these limiting cases, one can obtain the correlations exactly and we find excellent agreement with the direct Toda simulation results. We also discuss a transformation to "normal mode" variables, as commonly done in hydrodynamic theory of non-integrable systems, and find that this is useful, to some extent, even for the integrable system.

13 pages, 24 figures

References in corpus (5)

• Heat Transport in low-dimensional systems
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Heat transport in ordered harmonic lattices

Cited by in corpus (5)

• Anomalous heat transport in classical many-body systems: overview and perspectives
• Transport properties of the classical Toda chain: effect of a pinning potential
• Hydrodynamic Equations for the Toda Lattice
• KPZ modes in $d$-dimensional directed polymers
• Delocalization and heat transport in multidimensional trapped ion systems