21 research outputs found
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 -periodic
fluctuations as a function of the phase difference of the
superconductors. If the coupling to the superconductors is weak compared to the
coupling to the normal metals, the -dependence of the conductance is
harmonic, as observed in the experiment. In the opposite regime, the
conductance becomes a random -periodic function of , 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.
Conductance fluctuations and weak localization in chaotic quantum dots
We study the conductance statistical features of ballistic electrons flowing
through a chaotic quantum dot. We show how the temperature affects the
universal conductance fluctuations by analyzing the influence of dephasing and
thermal smearing. This leads us to two main findings. First, we show that the
energy correlations in the transmission, which were overlooked so far, are
important for calculating the variance and higher moments of the conductance.
Second, we show that there is an ambiguity in the method of determination of
the dephasing rate from the size of the of the weak localization. We find that
the dephasing times obtained at low temperatures from quantum dots are
underestimated.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let
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