Out-of-equilibrium Anderson model at high and low bias voltages

TL;DR

This paper investigates the out-of-equilibrium Anderson model for quantum dots, revealing how the Green's function behaves similarly to equilibrium cases at high and low bias voltages, and showing the adiabatic treatment of Coulomb interactions in these limits.

Contribution

It introduces a functional approach using the Keldysh formalism to analyze the Green's function dependence on bias voltage and temperature in out-of-equilibrium conditions.

Findings

High-voltage Green's function matches high-temperature equilibrium Green's function.

Low-voltage Green's function follows local Fermi-liquid theory up to (eV)^2 terms.

Correlation effects can be treated adiabatically at both voltage extremes.

Abstract

We study the high- and low-voltage properties of the out-of-equilibrium Anderson model for quantum dots, using a functional method in the Keldysh formalism. The Green's function at the impurity site can be regarded as a functional of a nonequilibrium distribution function. The dependence of the Green's function on the bias voltage V and temperature T arises through the nonequilibrium distribution function. From this behavior as a functional, it is shown that the nonequilibrium Green's function at high-voltage limit is identical to the equilibrium Green's function at high-temperature limit. This correspondence holds when the couplings of the dot and two leads, at the left and right, are equal. In the opposite limit, for small eV, the low-energy behavior of the Green's function can be described by the local Fermi-liquid theory up to terms of order $(eV)^2$. These results imply that the correlation effects due to the Coulomb interaction U can be treated adiabatically in the two limits, at high and low bias voltages.