Non-equilibrium dynamics of the Anderson impurity model

TL;DR

This paper investigates the non-equilibrium behavior of the M-channel Anderson impurity model under finite bias using the Non-Crossing Approximation, providing insights into conductance scaling and comparing theoretical approaches.

Contribution

It introduces an effective method to solve NCA equations at very low temperatures and derives a general formula connecting tunnel junctions and point contacts.

Findings

Conductance depends on bias via a universal scaling function.

The method enables analysis at temperatures well below the Kondo scale.

Comparison between conformal field theory and NCA self-energies for the two-channel case.

Abstract

The M-channel Anderson impurity model (M=1,2) is studied in the Kondo limit with a finite voltage bias applied to the conduction electron reservoirs. Using the Non-Crossing Approximation (NCA), we calculate the local spectral functions, the differential conductance, and susceptibility at non-zero bias for symmetric as well as asymmetric coupling of the impurity to the leads. We describe an effective procedure to solve the NCA integral equations which enables us to reach temperatures far below the Kondo scale. This allows us to study the scaling regime where the conductance depends on the bias only via a scaling function. Our results are applicable to both tunnel junctions and to point contacts. We present a general formula which allows one to go between the two cases of tunnel junctions and point contacts. Comparison is also made between the conformal field theory and the NCA conduction electron self-energies in the two channel case.