Dynamics of Energy Transport in a Toda Ring

TL;DR

This paper investigates energy transport and persistent currents in the classical Toda ring, examining how perturbations affect current decay and analyzing wave properties related to nonlinearity and integrability.

Contribution

It provides new insights into the relationship between conservation laws and persistent currents, and explores how perturbations influence energy transport in the Toda ring.

Findings

Persistent currents are linked to conservation laws.

Perturbations cause decay of currents over time.

Wave properties depend on nonlinearity and wave vector.

Abstract

We present results on the relationships between persistent currents and the known conservation laws in the classical Toda ring. We also show that perturbing the integrability leads to a decay of the currents at long times, with a time scale that is determined by the perturbing parameter. We summarize several known results concerning the Toda ring in 1-dimension, and present new results relating to the frequency, average kinetic and potential energy, and mean square displacement in the cnoidal waves, as functions of the wave vector and a parameter that determines the non linearity.