Disordered mesoscopic systems with interactions: induced two-body ensembles and the Hartree-Fock approach

Details Disordered mesoscopic systems with interactions: induced two-body ensembles and the Hartree-Fock approach Disordered mesoscopic systems with interactions: induced two-body ensembles and the Hartree-Fock approach

2004-06-22

arxiv.org/abs/cond-mat/0406495v1

Phys. Rev. B 72 (2005) 045318

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

25 pages, 16 figures

Scientific paper

10.1103/PhysRevB.72.045318

We introduce a generic approach to study interaction effects in diffusive or chaotic quantum dots in the Coulomb blockade regime. The randomness of the single-particle wave functions induces randomness in the two-body interaction matrix elements. We classify the possible induced two-body ensembles, both in the presence and absence of spin degrees of freedom. The ensembles depend on the underlying space-time symmetries as well as on features of the two-body interaction. Confining ourselves to spinless electrons, we then use the Hartree-Fock (HF) approximation to calculate HF single-particle energies and HF wave functions for many realizations of the ensemble. We study the statistical properties of the resulting one-body HF ensemble for a fixed number of electrons. In particular, we determine the statistics of the interaction matrix elements in the HF basis, of the HF single-particle energies (including the HF gap between the last occupied and the first empty HF level), and of the HF single-particle wave functions. We also study the addition of electrons, and in particular the distribution of the distance between successive conductance peaks and of the conductance peak heights.

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