Asymptotic Expansion for the Magnetoconductance Autocorrelation Function

We complement a recent calculation (P.B. Gossiaux and the present authors, Ann. Phys. (N.Y.) in press) of the autocorrelation function of the conductance versus magnetic field strength for ballistic electron transport through microstructures with the shape of a classically chaotic billiard coupled to ideal leads. The function depends on the total number M of channels and the parameter t which measures the difference in magnetic field strengths. We determine the leading terms in an asymptotic expansion for large t at fixed M, and for large M at fixed t/M. We compare our results and the ones obtained in the previous paper with the squared Lorentzian suggested by semiclassical theory.Comment: submitted to Annals of Physics (N.Y.

Level Repulsion in Constrained Gaussian Random-Matrix Ensembles

Introducing sets of constraints, we define new classes of random-matrix ensembles, the constrained Gaussian unitary (CGUE) and the deformed Gaussian unitary (DGUE) ensembles. The latter interpolate between the GUE and the CGUE. We derive a sufficient condition for GUE-type level repulsion to persist in the presence of constraints. For special classes of constraints, we extend this approach to the orthogonal and to the symplectic ensembles. A generalized Fourier theorem relates the spectral properties of the constraining ensembles with those of the constrained ones. We find that in the DGUEs, level repulsion always prevails at a sufficiently short distance and may be lifted only in the limit of strictly enforced constraints.Comment: 20 pages, no figures. New section adde

Spectral fluctuation properties of constrained unitary ensembles of Gaussian-distributed random matrices

We investigate the spectral fluctuation properties of constrained ensembles of random matrices (defined by the condition that a number N(Q) of matrix elements vanish identically; that condition is imposed in unitarily invariant form) in the limit of large matrix dimension. We show that as long as N(Q) is smaller than a critical value (at which the quadratic level repulsion of the Gaussian unitary ensemble of random matrices may be destroyed) all spectral fluctuation measures have the same form as for the Gaussian unitary ensemble.Comment: 15 page

Phase-dependent magnetoconductance fluctuations in a chaotic Josephson junction

Motivated by recent experiments by Den Hartog et al., we present a random-matrix theory for the magnetoconductance fluctuations of a chaotic quantum dot which is coupled by point contacts to two superconductors and one or two normal metals. There are aperiodic conductance fluctuations as a function of the magnetic field through the quantum dot and $2\pi$-periodic fluctuations as a function of the phase difference $\phi$ of the superconductors. If the coupling to the superconductors is weak compared to the coupling to the normal metals, the $\phi$-dependence of the conductance is harmonic, as observed in the experiment. In the opposite regime, the conductance becomes a random $2\pi$-periodic function of $\phi$, in agreement with the theory of Altshuler and Spivak. The theoretical method employs an extension of the circular ensemble which can describe the magnetic field dependence of the scattering matrix.Comment: 4 pages, RevTeX, 3 figure

Estimating the nuclear level density with the Monte Carlo shell model

A method for making realistic estimates of the density of levels in even-even nuclei is presented making use of the Monte Carlo shell model (MCSM). The procedure follows three basic steps: (1) computation of the thermal energy with the MCSM, (2) evaluation of the partition function by integrating the thermal energy, and (3) evaluating the level density by performing the inverse Laplace transform of the partition function using Maximum Entropy reconstruction techniques. It is found that results obtained with schematic interactions, which do not have a sign problem in the MCSM, compare well with realistic shell-model interactions provided an important isospin dependence is accounted for.Comment: 14 pages, 3 postscript figures. Latex with RevTex. Submitted as a rapid communication to Phys. Rev.

Coulomb blockade conductance peak fluctuations in quantum dots and the independent particle model

We study the combined effect of finite temperature, underlying classical dynamics, and deformations on the statistical properties of Coulomb blockade conductance peaks in quantum dots. These effects are considered in the context of the single-particle plus constant-interaction theory of the Coulomb blockade. We present numerical studies of two chaotic models, representative of different mean-field potentials: a parametric random Hamiltonian and the smooth stadium. In addition, we study conductance fluctuations for different integrable confining potentials. For temperatures smaller than the mean level spacing, our results indicate that the peak height distribution is nearly always in good agreement with the available experimental data, irrespective of the confining potential (integrable or chaotic). We find that the peak bunching effect seen in the experiments is reproduced in the theoretical models under certain special conditions. Although the independent particle model fails, in general, to explain quantitatively the short-range part of the peak height correlations observed experimentally, we argue that it allows for an understanding of the long-range part.Comment: RevTex 3.1, 34 pages (including 13 EPS and PS figures), submitted to Phys. Rev.

Random-Matrix Theory of Quantum Transport

This is a comprehensive review of the random-matrix approach to the theory of phase-coherent conduction in mesocopic systems. The theory is applied to a variety of physical phenomena in quantum dots and disordered wires, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction.Comment: 85 pages including 52 figures, to be published in Rev.Mod.Phy