COMPRESSIBILITY, CAPACITANCE, AND GROUND-STATE ENERGY FLUCTUATIONS INA WEAKLY INTERACTING QUANTUM-DOT

We study the effect of electron-electron (e-e) interactions on compres sibility, capacitance, and inverse compressibility of electrons in a q uantum dot or a small metallic grain. The calculation is performed in the random-phase approximation. As expected, the ensemble-averaged com pressibility and capacitance decreases as a function of the interactio n strength, while the mean inverse compressibility increases. Fluctuat ions of the compressibility are found to be strongly suppressed by the e-e interactions. Fluctuations of the capacitance and inverse compres sibility also turn out to be much smaller than their averages. The ana lytical calculations are compared with the results of a numerical calc ulation for the inverse compressibility of a disordered tight-binding model. Excellent agreement for weak-interaction values is found. Impli cations for the interpretation of current experimental data are discus sed.