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We derive a universal Hamiltonian for a quantum dot in the presence of spin-orbit interaction in the symmetry limits of a strong spin-dependent Aharonov-Bohm-like term. We also derive a closed expression for the conductance through such a dot, and use it to study the effects of spin-orbit on the conductance peak statistics in the presence of an exchange interaction. For a realistic strength of the exchange interaction, we find that the width of the peak-spacing distribution is sensitive to spin-orbit coupling only in the absence of an orbital magnetic field. We also find that spin-orbit coupling modifies the shape of the peak-spacing distribution and suppresses the peak-height fluctuations., Comment: 4 pages, 2 figures

We derive a closed expression for the linear conductance through a quantum dot in the Coulomb-blockade regime in the presence of a constant exchange interaction. With this expression we calculate the temperature dependence of the conductance peak-height and peak-spacing statistics. Using a realistic value of the exchange interaction, we find significantly better agreement with experimental data as compared with the statistics obtained in the absence of an exchange interaction., Comment: 4 pages, 4 figures, revtex4, typos corrected

We discuss the calculation of the linear conductance through a Coulomb-blockade quantum dot in the presence of interactions beyond the charging energy. In the limit where the temperature is large compared with a typical tunneling width, we use a rate-equations approach to describe the transitions between the corresponding many-body states. We discuss both the elastic and rapid-thermalization limits, where the rate of inelastic scattering in the dot is either small or large compared with the elastic transition rate, respectively. In the elastic limit, we find several cases where a closed solution for the conductance is possible, including the case of a constant exchange interaction. In the rapid-thermalization limit, a closed solution is possible in the general case. We show that the corresponding expressions for the linear conductance simplify for a Hamiltonian that is invariant under spin rotations., Comment: 11 pages, no figures, revtex4

We calculate the finite-temperature conductance peak-height distributions in Coublomb-blockade quantum dots in the limit where the inelastic scattering rate in the dot is large compared with the mean elastic tunneling rate. The relative reduction of the standard deviation of the peak-height distribution by a time-reversal symmetry-breaking magnetic field, which is essentially temperature-independent in the elastic limit, is enhanced by the inclusion of inelastic scattering at finite temperature. We suggest this quantity as an independent experimental probe for inelastic scattering in closed dots., Comment: 4 pages, 3 eps figures, revtex4

We consider $m$ spinless Bosons distributed over $l$ degenerate single-particle states and interacting through a $k$-body random interaction with Gaussian probability distribution (the Bosonic embedded $k$-body ensembles). We address the cases of orthogonal and unitary symmetry in the limit of infinite matrix dimension, attained either as $l \to \infty$ or as $m \to \infty$. We derive an eigenvalue expansion for the second moment of the many-body matrix elements of these ensembles. Using properties of this expansion, the supersymmetry technique, and the binary correlation method, we show that in the limit $l \to \infty$ the ensembles have nearly the same spectral properties as the corresponding Fermionic embedded ensembles. Novel features specific for Bosons arise in the dense limit defined as $m \to \infty$ with both $k$ and $l$ fixed. Here we show that the ensemble is not ergodic, and that the spectral fluctuations are not of Wigner-Dyson type. We present numerical results for the dense limit using both ensemble unfolding and spectral unfolding. These differ strongly, demonstrating the lack of ergodicity of the ensemble. Spectral unfolding shows a strong tendency towards picket-fence type spectra. Certain eigenfunctions of individual realizations of the ensemble display Fock-space localization., Comment: Minor corrections; figure 5 slightly modified (30 pages, 6 figs)

We investigate the shape of the spectrum and the spectral fluctuations of the $k$-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the number of Bosons $m \to \infty$ while both $k$, the rank of the interaction, and $l$, the number of single-particle states, are kept fixed. We show that the relative fluctuations of the low spectral moments do not vanish in this limit, proving that the ensemble is non-ergodic. Numerical simulations yield spectra which display a strong tendency towards picket-fence type. The wave functions also deviate from canonical random-matrix behaviour, Comment: 7 pages, 5 figures, uses epl.cls (included)

We investigate the properties of sparse matrix ensembles with particular regard for the spectral ergodicity hypothesis, which claims the identity of ensemble and spectral averages of spectral correlators. An apparent violation of the spectral ergodicity is observed. This effect is studied with the aid of the normal modes of the random matrix spectrum, which describe fluctuations of the eigenvalues around their average positions. This analysis reveals that spectral ergodicity is not broken, but that different energy scales of the spectra are examined by the two averaging techniques. Normal modes are shown to provide a useful complement to traditional spectral analysis with possible applications to a wide range of physical systems., Comment: 22 pages, 15 figures