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Journal Article

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


Weidenmüller,  Hans A.
Prof. Hans A. Weidenmüller, Emeriti, MPI for Nuclear Physics, Max Planck Society;

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Alhassid, Y., Weidenmüller, H. A., & Wobst, A. (2005). Disordered mesoscopic systems with interactions: Induced two-body ensembles and the Hartree-Fock approach. Physical Review A, 72: 045318. doi:10.1103/PhysRevB.72.045318.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0011-8897-A
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.