Ullmo, D; Baranger, HU, *Interactions in chaotic nanoparticles: Fluctuations in Coulomb blockade peak spacings*,
Physical Review. B, Condensed Matter, vol. 64 no. 24
(2001),
pp. 2453241-24532413 [0103098v1], [doi] .
**Abstract:**

*We use random matrix models and a Fermi-liquid approach to investigate the ground state energy of electrons confined to a nanoparticle. Our expression for the energy includes the charging effect, the single-particle energies, and the residual screened interactions treated in Hartree-Fock. This model is applicable to chaotic quantum dots or nanoparticles - in these systems the single-particle statistics follows random matrix theory at energy scales less than the Thouless energy. We find the distribution of Coulomb blockade peak spacings first for a large dot in which the residual interactions can be taken constant: the spacing fluctuations are of order the mean level separation Δ. Corrections to this limit are studied using the small parameter 1/kFL: both the residual interactions and the effect of the changing confinement on the single-particle levels produce fluctuations of order Δ/√kFL. The distributions we find are qualitatively similar to the experimental results. Thus, models beyond Fermi-liquid theory are not needed to describe this quantity.*