Mesoscopic Anderson Box: Connecting Weak to Strong Coupling

TL;DR

This paper explores how mesoscopic fluctuations in Anderson impurity systems evolve from weak to strong coupling, revealing universal behaviors and small mean field fluctuations through random matrix theory and SBMFA.

Contribution

It connects weak and strong coupling regimes in Anderson impurity problems by analyzing fluctuations and universality using RMT and SBMFA, providing new insights into mesoscopic impurity physics.

Findings

Universal distributions of energy levels within the Kondo resonance.

Small fluctuations of mean field parameters in SBMFA.

Strong impurity effects significantly alter wave functions but retain correlations.

Abstract

Both the weakly coupled and strong coupling Anderson impurity problems are characterized by a Fermi-liquid theory with weakly interacting quasiparticles. In an Anderson box, mesoscopic fluctuations of the effective single particle properties will be large. We study how the statistical fluctuations at low temperature in these two problems are connected, using random matrix theory and the slave boson mean field approximation (SBMFA). First, for a resonant level model such as results from the SBMFA, we find the joint distribution of energy levels with and without the resonant level present. Second, if only energy levels within the Kondo resonance are considered, the distributions of perturbed levels collapse to universal forms for both orthogonal and unitary ensembles for all values of the coupling. These universal curves are described well by a simple Wigner-surmise type toy model. Third, we study the fluctuations of the mean field parameters in the SBMFA, finding that they are small. Finally, the change in the intensity of an eigenfunction at an arbitrary point is studied, such as is relevant in conductance measurements: we find that the introduction of the strongly-coupled impurity considerably changes the wave function but that a substantial correlation remains.