Mixed-state aspects of an out-of-equilibrium Kondo problem in a quantum dot

TL;DR

This paper investigates the nonequilibrium steady state of a quantum dot Kondo problem using a reduced density matrix approach, revealing mixed-state characteristics and the effects of Coulomb interactions.

Contribution

It introduces a method to analyze the nonequilibrium Kondo problem via a reduced density matrix in Fock space, highlighting mixed-state properties and symmetry effects.

Findings

In the noninteracting case, the system exhibits mixed states similar to high-temperature equilibrium distributions.

Coulomb interactions preserve the mixed-state characteristics and allow correlation functions to be expressed in Lehmann-representation.

Inversion symmetry leads to random occupation of states between chemical potentials, affecting the steady state.

Abstract

We reexamine basic aspects of a nonequilibrium steady state in the Kondo problem for a quantum dot under a bias voltage using a reduced density matrix, which is obtained in the Fock space by integrating out one of the two conduction channels. The integration has been carried out by discretizing the conduction channels preserving the two-fold degeneracy due to the left-going and right-going scattering states. The remaining subspace is described by a single-channel Anderson model, and the statistical weight is determined by the reduced density matrix. In the noninteracting case, it can be constructed as the mixed states that show a close similarity to the high-temperature distribution in equilibrium. Specifically, if the system has an inversion symmetry, the one-particle states in an energy window between the two chemical potentials \mu_R and \mu_L are occupied, or unoccupied, completely at random with an equal weight. The Coulomb interaction preserves these aspects, and the correlation functions can be expressed in a Lehmann-representation form using the mixed-state statistical weight.