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.

arXiv comment13 pages, 24 figures

References in corpus (22)

• Thermal conduction in classical low-dimensional lattices
• Heat Transport in low-dimensional systems
• Canonical Typicality
• Generalized Gibbs ensemble in integrable lattice models
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Exact results for anomalous transport in one dimensional Hamiltonian systems
• Heat conduction in the diatomic Toda lattice revisited
• Anomalous Heat Diffusion
• Anomalous Heat Diffusion
• Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
• Universal Large Deviations for the Tagged Particle in Single File Motion
• Equilibrium time-correlation functions for one-dimensional hard-point systems
• Absence of local thermal equilibrium in two models of heat conduction
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Eigenstate Gibbs Ensemble in Integrable Quantum Systems
• Heat transport in ordered harmonic lattices
• Anomalous fluctuations for a perturbed Hamiltonian system with exponential interactions
• Thermal conductivity of the Toda lattice with conservative noise
• Dynamics of Energy Transport in a Toda Ring

Cited by in corpus (26)

• Lecture notes on Generalised Hydrodynamics
• Generalised hydrodynamics of the classical Toda system
• Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
• Generalized Gibbs Ensembles of the classical Toda chain
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Non-Fourier heat transport in nanosystems
• Interacting and noninteracting integrable systems
• Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs
• Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain
• Transport in perturbed classical integrable systems: the pinned Toda chain
• Entropy growth during free expansion of an ideal gas
• Transport properties of the classical Toda chain: effect of a pinning potential
• Hydrodynamic Equations for the Toda Lattice
• Dynamics of fluctuation correlation in periodically driven classical system
• Using Hilbert transform and classical chains to simulate quantum walks
• Ballistic space-time correlators of the classical Toda lattice
• Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale
• Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
• Heat perturbations spreading in the Fermi-Pasta-Ulam-$\beta$ system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity
• KPZ modes in $d$-dimensional directed polymers
• Semiclassical Limit of Measurement-Induced Transition in Many-Body Chaos in Integrable and Nonintegrable Oscillator Chains
• Delocalization and heat transport in multidimensional trapped ion systems
• Correlation Functions for a Chain of Short Range Oscillators
• Integrable hydrodynamics of Toda chain: case of small systems
• Lax dynamics
• Dynamical correlations of conserved quantities in the one-dimensional equal mass hard particle gas