A quantum dot is a sub-micron-scale conducting device containing up to several thousand electrons. Transport through a quantum dot at low temperatures is a quantum-coherent process. This review focuses on dots in which the electron's dynamics are chaotic or diffusive, giving rise to statistical properties that reflect the interplay between one-body chaos, quantum interference, and electronelectron interactions. The conductance through such dots displays mesoscopic fluctuations as a function of gate voltage, magnetic field, and shape deformation. The techniques used to describe these fluctuations include semiclassical methods, random-matrix theory, and the supersymmetric nonlinear σ model. In open dots, the approximation of noninteracting quasiparticles is justified, and electron-electron interactions contribute indirectly through their effect on the dephasing time at finite temperature. In almost-closed dots, where conductance occurs by tunneling, the charge on the dot is quantized, and electron-electron interactions play an important role. Transport is dominated by Coulomb blockade, leading to peaks in the conductance that at low temperatures provide information on the dot's ground-state properties. Several statistical signatures of electronelectron interactions have been identified, most notably in the dot's addition spectrum. The dot's spin, determined partly by exchange interactions, can also influence the fluctuation properties of the conductance. Other mesoscopic phenomena in quantum dots that are affected by the charging energy include the fluctuations of the cotunneling conductance and mesoscopic Coulomb blockade.[Published in Rev. Mod. Phys. 72, 895 (2000)] 2. Random-phase approximation in disordered dots 56 3. Parametric variation of the mean field 57 4. Anderson model with interactions 58 B. Spin effects and interactions 58 C. Peak-height statistics and interactions 61 D. Random interaction matrix model 62 VII. Charging Energy Effects in Quantum Dots 64 A. Mesoscopic fluctuations in elastic cotunneling 64 B. Mesoscopic Coulomb blockade 66 C. Mesoscopic fluctuations of the differential capacitance 68 VIII. Conclusion and Future Directions 69 IX. Acknowledgments 72 References 72

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We present a practical solution to the "sign problem" in the auxiliary field Monte Carlo approach to the nuclear shell model. The method is based on extrapolation from a continuous family of problem-free Hamiltonians. To demonstrate the resultant ability to treat large shell-model problems, we present results for 54 Fe in the full f p-shell basis using the Brown-Richter interaction. We find the Gamow-Teller β + strength to be quenched by 58% relative to the single-particle estimate, in better agreement with experiment than previous estimates based on truncated bases.

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Total and parity-projected level densities of iron-region nuclei are calculated microscopically by using Monte Carlo methods for the nuclear shell model in the complete (pf + 0g 9/2 )-shell. The calculated total level density is found to be in good agreement with the experimental level density. The Monte Carlo calculations offer a significant improvement over the thermal Hartree-Fock approximation. Contrary to the Fermi gas model, it is found that the level density has a significant parity-dependence in the neutron resonance region. The systematics of the level density parameters (including shell effects) in the iron region is presented.