Interaction Matrix Element Fluctuations in Ballistic Quantum Dots: Random Wave Model
arXiv:0802.2410 · doi:10.1103/PhysRevB.78.085305
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 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 strongly non-Gaussian distributions, despite the Gaussian random nature of the single-electron wave functions.
13 pages, 10 figures
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