Mesoscopic Kondo Problem

TL;DR

This paper investigates how mesoscopic fluctuations influence the Kondo effect in confined electron systems, revealing that perturbative methods are effective above the Kondo temperature, but fluctuations become significant below it.

Contribution

It demonstrates the applicability of perturbative techniques to analyze mesoscopic fluctuations in Kondo systems and compares these with exact Quantum Monte Carlo results.

Findings

Perturbative methods capture fluctuations well above the Kondo temperature.

Large fluctuations and deviations from universality occur below the Kondo temperature.

Semi-classical approximations enable wide-ranging calculations of mesoscopic fluctuations.

Abstract

We study the effect of mesoscopic fluctuations on a magnetic impurity coupled to a spatially confined electron gas with a temperature in the mesoscopic range (i.e. between the mean level spacing $\Delta$ and the Thouless energy $E_{\rm Th}$). Comparing ``poor-man's scaling'' with exact Quantum Monte Carlo, we find that for temperatures larger than the Kondo temperature, many aspects of the fluctuations can be captured by the perturbative technique. Using this technique in conjunction with semi-classical approximations, we are able to calculate the mesoscopic fluctuations for a wide variety of systems. For temperatures smaller than the Kondo temperature, we find large fluctuations and deviations from the universal behavior.