Properties of Low-Lying States in a Diffusive Quantum Dot and Fock-Space Localization

Motivated by an experiment by Sivan et al. [Europhys. Lett. 25, 605 (1994)] and by subsequent theoretical work on localization in Fock space, we study numerically a hierarchical model for a finite many-body system of fermions moving in a disordered potential and coupled by a two-body interaction. We focus attention on the low-lying states close to the Fermi energy. Both the spreading width and the participation number depend smoothly on excitation energy. This behavior is in keeping with naive expectations and does not display Anderson localization. We show that the model reproduces essential features of the experiment by Sivan et al.