Statistical Properties of The First Excited State of an Interacting Many Particle Disordered System

Abstract

The distribution $P_1$ of the first many-body excitation energy of a weakly and moderately interacting electron gas in a finite conductor (in the diffusive regime) is calculated. As the interaction is increased, $P_1$ crosses over from Wigner-Dyson to Poisson. We characterize this transition through the inverse participation ratio in Hilbert space, and examine its manifestation in a projected 2-dimensional space.

arXiv comment5 pages, 5 figures, corrected abstract posting

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• Critiquing Variational Theories of the Anderson-Hubbard Model: Real-Space Self-Consistent Hartree-Fock Solutions
• Energy Level Statistics of Quantum Dots