Coulomb Charging Effects for Finite Channel Number

TL;DR

This paper investigates how quantum charge fluctuations in small metallic grains depend on the number of tunneling channels, revealing rapid convergence to classical behavior as channels increase.

Contribution

It provides a detailed analysis of Coulomb charging effects for finite channel numbers, extending previous results for large N to smaller N regimes.

Findings

Charging effects diminish quickly as the number of channels increases.

The average charge and charging energy approach classical limits with increasing N.

Results bridge the gap between quantum and classical descriptions for small metallic grains.

Abstract

We consider quantum fluctuations of the charge on a small metallic grain caused by virtual electron tunneling to a nearby electrode. The average electron number and the effective charging energy are determined by means of perturbation theory in the tunneling Hamiltonian. In particular we discuss the dependence of charging effects on the number N of tunneling channels. Earlier results for N>>1 are found to be approached rather rapidly with increasing N.