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Phys. Rev. B 76, 195448 (2007) [16 pages]

Level spacings in random matrix theory and Coulomb blockade peaks in quantum dots

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Damir Herman1,*, T. Tzen Ong2,†, Gonzalo Usaj2,3, Harsh Mathur1, and Harold U. Baranger2
1Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-7079, USA
2Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708, USA
3Instituto Balseiro and Centro Atómico Bariloche, Comisión Nacional de Energia Atómica, 8400 Bariloche, Argentina

Received 12 July 2007; revised 18 August 2007; published 30 November 2007

We obtain analytic formulas for the spacing between conductance peaks in the Coulomb blockade regime based on the universal Hamiltonian model of quantum dots. Random matrix theory results are developed in order to treat correlations between two and three consecutive spacings in the energy level spectrum. These are generalizations of the Wigner surmise for the probability distribution of single level spacing. The analytic formulas are shown to be in good agreement with numerical evaluation.

© 2007 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevB.76.195448
DOI:
10.1103/PhysRevB.76.195448
PACS:
73.23.Hk, 05.45.Mt, 73.21.La, 02.10.Yn

*Present address: Myeloma Institute for Research and Therapy, University of Arkansas for Medical Sciences, Little Rock, AR 72205.

Present address: Dept. of Applied Physics, Stanford University, Stanford, CA 94305.