Anharmonic Oscillations, Dissipative Solitons and Non-Ohmic Supersonic Electric Transport

Abstract

We consider the Toda lattice Toda lattice with exponentially repulsive interactions between the units and view these units as Brownian elements capable of pumping energy from a surrounding heat bath or reservoir, and we show that solitons can be excited and maintained in the presence of dissipation. Then, we endow these Toda lattice units with electric charge, i.e., we make them positive ions and add free electrons to the system. We use this to show that, in the presence of an external electric field, following an instability of the base linear Ohm conduction state, the electromechanical Toda lattice is able to maintain a non-Ohmic soliton-driven supersonic electric current, and we then discuss its striking characteristics. Thus the lattice appears very much like a versatile neural transmission line.