Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2007-12-26
AIP Conf. Proc. 995, 192 (2008)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
12 pages, 6 figures; submitted for conference proceedings of Workshop on Nuclei and Mesoscopic Physics (WNMP07), October 20-22
Scientific paper
10.1063/1.2915599
In the Coulomb blockade regime of a ballistic quantum dot, the distribution of conductance peak spacings is well known to be incorrectly predicted by a single-particle picture; instead, matrix element fluctuations of the residual electronic interaction need to be taken into account. In the normalized random-wave model, valid in the semiclassical limit where the number of electrons in the dot becomes large, we obtain analytic expressions for the fluctuations of two-body and one-body matrix elements. However, these fluctuations may be too small to explain low-temperature experimental data. We have examined matrix element fluctuations in realistic chaotic geometries, and shown that at energies of experimental interest these fluctuations generically exceed by a factor of about 3-4 the predictions of the random wave model. Even larger fluctuations occur in geometries with a mixed chaotic-regular phase space. These results may allow for much better agreement between the Hartree-Fock picture and experiment. Among other findings, we show that the distribution of interaction matrix elements is strongly non-Gaussian in the parameter range of experimental interest, even in the random wave model. We also find that the enhanced fluctuations in realistic geometries cannot be computed using a leading-order semiclassical approach, but may be understood in terms of short-time dynamics.
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