Interaction matrix element fluctuations in ballistic quantum dots: Random wave model

L. Kaplan and Y. Alhassid
Phys. Rev. B 78, 085305 – Published 11 August 2008

Abstract

We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface-charge potential in ballistic quantum dots. For chaotic dots, we use a normalized random wave model to obtain analytic expansions for matrix element variances and covariances in the limit of large kL (where k is the Fermi wave number and L is the linear size of the dot). These leading-order analytical results are compared with exact numerical results. Both two-body and one-body matrix elements are shown to follow non-Gaussian distributions, in spite of the Gaussian random nature of the single-electron wave functions.

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  • Received 17 February 2008

DOI:https://doi.org/10.1103/PhysRevB.78.085305

©2008 American Physical Society

Authors & Affiliations

L. Kaplan1 and Y. Alhassid2

  • 1Department of Physics, Tulane University, New Orleans, Louisiana 70118, USA
  • 2Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520, USA

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Issue

Vol. 78, Iss. 8 — 15 August 2008

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