Ballistic transport in the classical Toda chain with harmonic pinning

TL;DR

This study uses numerical simulations to reveal that the classical Toda chain with harmonic pinning exhibits ballistic heat transport, challenging the expectation that non-momentum conserving systems are diffusive.

Contribution

It demonstrates that harmonic pinning in the Toda chain leads to ballistic transport, suggesting possible integrability or atypical behavior in non-momentum conserving systems.

Findings

Ballistic heat transport observed with harmonic pinning.

Energy current oscillates without decay on a ring.

System dynamics occur on a 3D manifold, indicating potential integrability.

Abstract

We investigate, via numerical simulation, heat transport in the nonequilibrium stationary state (NESS) of the 1D classical Toda chain with an additional pinning potential, which destroys momentum conservation. The NESS is produced by coupling the system, via Langevin dynamics, to two reservoirs at different temperatures. To our surprise, we find that when the pinning is harmonic, the transport is ballistic. We also find that on a periodic ring with nonequilibrium initial conditions and no reservoirs, the energy current oscillates without decay. Lastly, Poincar\'e sections of the 3-body case indicate that for all tested initial conditions, the dynamics occur on a 3-dimensional manifold. These observations suggest that the $N$-body Toda chain with harmonic pinning may be integrable. Alternatively, and more likely, this would be an example of a nonintegrable system without momentum conservation for which the heat flux is ballistic - contrary to all current expectations.