On the violation of Ohm's law for bounded interactions: a one-dimensional system (Q1885619)

The authors study a one-dimensional Hamiltonian system consisting of a charged particle under the action of a constant electric field and interacting with an infinite system of classical particles. The particles of the medium are initially assumed to be in an equilibrium Gibbs state. It is proved that for a suitable class of bounded interactions and each positive value of the electric field the average velocity of the charged particle increases linearly in time. This contradicts Ohm's law, according to which the drift is proportional to the electric field. The authors treated this problem for large electric fields already in a previous paper [Commun. Math. Phys. 233, No. 3, 545--569 (2003; Zbl 1034.82040)].