Energy current and energy fluctuations in driven quantum wires

TL;DR

This paper investigates energy currents and fluctuations in a driven quantum wire of interacting spinless fermions, revealing behaviors from linear response to damping oscillations due to heating effects.

Contribution

It introduces a detailed analysis of energy transport and fluctuations in a non-equilibrium quantum wire, including the effects of Joule heating and Bloch oscillations.

Findings

Energy current aligns with linear response at weak driving.

System exhibits damping of energy current under strong driving.

Energy spread increases with driving, showing unexpected time dependence.

Abstract

We discuss the energy current and the energy fluctuations in an isolated quantum wire driven far from equilibrium. The system consists of interacting spinless fermions and is driven by a time--dependent magnetic flux. The energy current is defined by the continuity equation for the energy density which is derived both for homogeneous as well as for inhomogeneous systems. Since the total energy is not conserved in the driven system, the continuity equation includes the source terms which are shown to represent the Joule heating effects. For short times and weak drivings the energy current agrees with the linear response theory. For stronger fields or longer times of driving the system enters the quasiequilibrium regime when the energy current gradually diminishes due to the heating effects. Finally, for even stronger driving the energy current is shown to undergo a damped Bloch oscillations. The energy spread also increases upon driving. However, the time--dependence of this quantity in the low field regime is quite unexpected since it is determined mostly by the time of driving being quite independent of the instantaneous energy of the system.