The addition spectrum of a classical short-range interaction model for a disordered quantum dot

The addition spectrum of a classical short-range interaction model for a disordered quantum dot is calculated numerically. The average change in the chemical potential needed to add a particle, as well as the fluctuations in this quantity, are proportional to the interaction strength, and their ratio is one for a wide range of interaction strengths. Analytical arguments which lead to the same result are also presented. On the basis of these results the behaviour of these quantities for real Coulomb interactions at the high-density limit may be reproduced, and speculations on the behaviour at low densities are presented.