g-Factors and Discrete Energy Level Velocities in Nanoparticles

TL;DR

This paper derives relations linking g-factor statistics and energy level velocity fluctuations in metallic nanoparticles with spin-orbit coupling, assuming chaotic electron dynamics, enabling experimental comparison without adjustable parameters.

Contribution

It introduces a theoretical framework connecting g-factor fluctuations to energy level velocities in nanoparticles with spin-orbit coupling, assuming chaotic electron behavior.

Findings

Derived expressions linking g factor second moment to level velocity RMS

Provided parameter-free predictions for experimental validation

Connected observable quantities to underlying quantum chaos phenomena

Abstract

We establish relations between the statistics of g factors and the fluctuations of energy in metallic nanoparticles where spin-orbit coupling is present. These relations assume that the electron dynamics in the grain is chaotic. The expressions we provide connect the second moment of the g factor to the root-mean square ``level velocity'' (the derivative of the energy with respect to magnetic field) calculated at magnetic fields larger than a characteristic correlation field. Our predictions relate readily observable quantities and allow for a parameter-free comparison with experiments.