Transport properties of the classical Toda chain: effect of a pinning potential

Abstract

We consider energy transport in the classical Toda chain in the presence of an additional pinning potential. The pinning potential is expected to destroy the integrability of the system and an interesting question is to see the signatures of this breaking of integrability on energy transport. We investigate this by a study of the non-equilibrium steady state of the system connected to heat baths as well as the study of equilibrium correlations. Typical signatures of integrable systems are a size-independent energy current, a flat bulk temperature profile and ballistic scaling of equilibrium dynamical correlations, these results being valid in the thermodynamic limit. We find that, as expected, these properties change drastically on introducing the pinning potential in the Toda model. In particular, we find that the effect of a harmonic pinning potential is drastically smaller at low temperatures, compared to a quartic pinning potential. We explain this by noting that at low temperatures the Toda potential can be approximated by a harmonic inter-particle potential for which the addition of harmonic pinning does not destroy integrability.

9 Pages,12 figures

References in corpus (5)

• Heat Transport in low-dimensional systems
• Local Temperature and Universal Heat Conduction in FPU chains
• Non-integrability and the Fourier heat conduction law
• Heat transport in ordered harmonic lattices
• Equilibrium dynamical correlations in the Toda chain and other integrable models

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