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Title:
Universality in ultra-small metallic grains
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Abstract:
The single-particle Hamiltonian of a nano-scale metallic grain (nanoparticle) with irregular boundaries or weak disorder is described by random-matrix theory. We show that the randomness of the single-particle wave functions induces a randomness in the two-body interaction matrix elements, and leads to a description of the interaction in terms of a leading-order universal Hamiltonian and an induced two-body random-matrix ensemble that are determined by the underlying space-time symmetries. We discuss universal fluctuations in transport and in thermodynamic properties of the nanoparticle. Of particular interest is the fluctuation-dominated regime, in which the BCS theory of superconductivity breaks down. We also discuss effects of the induced two-body random-matrix ensemble.
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