# AC quantum transport: Non-equilibrium in mesoscopic wires due to time-dependent fields

## TL;DR

This paper models the non-equilibrium energy distribution of quasi-particles in a mesoscopic normal metal wire under time-dependent ac bias, revealing how high-frequency irradiation and interactions influence charge transport and energy states.

## Contribution

It introduces a Green function-based quantum diffusion model for ac-driven mesoscopic wires, analyzing photon absorption effects and the impact of electron-electron and electron-phonon interactions on energy distributions.

## Key findings

- Photon steps depend on field amplitude and photon energy.
- In slow field regime, photon absorption is time-dependent.
- Strong interactions lead to Fermi distributions with bath or effective temperature.

## Abstract

A model is developed describing the energy distribution of quasi-particles in a quasi-one dimensional, normal metal wire, where the transport is diffusive, connected between equilibrium reservoirs. When an ac bias is applied to the wire by means of the reservoirs, the statistics of the charge carriers is influence by the formed non-equilibrium. The proposed model is derived from Green function formalism. The quasi-particle energy distribution is calculated with a quantum diffusion equation including a collision term accounting for inelastic scattering. The ac bias, due to high frequency irradiation, drives the wire out of equilibrium. For coherent transport the photon absorption processes create multiple photon steps in the energy distribution, where the number of steps is dependent on the relation between the amplitude of the field eV and the photon energy \omega. Furthermore we observe that for the slow field regime, \omega \tau_D < 1, the photon absorption is highly time-dependent. In the fast field regime \omega \tau_D > 1 this time-dependency disappears and the photon steps in the distribution have a fixed value. When the wire is extended, the transport becomes incoherent due to interaction processes, like electron-electron interaction and electron-phonon interaction. These interactions give rise to a redistribution of the quasi-particles with respect to the energy. We focused on the fast field regime and concluded that the strong interaction limit for both mechanisms gives the expected result. Strong electron-phonon interaction forces the distribution function on every position in the wire to become a Fermi function with the bath temperature, while strong electron-electron interaction causes an effective temperature profile across the wire and the distribution function on every position in the wire is a Fermi function with an effective temperature.