Dynamics of Energy Transport in a Toda Ring

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.

34 pages, 11 figures. Small changes made in response to referee's comments

References in corpus (3)

• Optimized Forest-Ruth- and Suzuki-like algorithms for integration of motion in many-body systems
• Spin conductivity in almost integrable spin chains
• Solitons on H-bonds in proteins

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