  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.
