Interaction Matrix Element Fluctuations in Ballistic Quantum Dots: Random Wave Model

Details Interaction Matrix Element Fluctuations in Ballistic Quantum Dots: Random Wave Model Interaction Matrix Element Fluctuations in Ballistic Quantum Dots: Random Wave Model

2008-02-18

arxiv.org/abs/0802.2410v1

Phys. Rev. B 78, 085305 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

13 pages, 10 figures

Scientific paper

10.1103/PhysRevB.78.085305

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.

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