27 research outputs found
Statistics of Coulomb Blockade Peak Spacings within the Hartree-Fock Approximation
We study the effect of electronic interactions on the addition spectra and on
the energy level distributions of two-dimensional quantum dots with weak
disorder using the self-consistent Hartree-Fock approximation for spinless
electrons. We show that the distribution of the conductance peak spacings is
Gaussian with large fluctuations that exceed, in agreement with experiments,
the mean level spacing of the non-interacting system. We analyze this
distribution on the basis of Koopmans' theorem. We show furthermore that the
occupied and unoccupied Hartree-Fock levels exhibit Wigner-Dyson statistics.Comment: 5 pages, 2 figures, submitted for publicatio
Conductivity fluctuations in polymer's networks
Polymer's network is treated as an anisotropic fractal with fractional
dimensionality D = 1 + \epsilon close to one. Percolation model on such a
fractal is studied. Using the real space renormalization group approach of
Migdal and Kadanoff we find threshold value and all the critical exponents to
be strongly nonanalytic functions of \epsilon, e.g. the critical exponent of
the conductivity was obtained to be \epsilon^{-2}\exp(-1-1/\epsilon). The main
part of the finite size conductivities distribution function at the threshold
was found to be universal if expressed in terms of the fluctuating variable,
which is proportional to the large power of the conductivity, but with
dimensionally-dependent low-conductivity cut-off. Its reduced central momenta
are of the order of \exp(-1/\epsilon) up to the very high order.Comment: 7 pages, one eps figure, uses epsf style, to be published in Proc. of
LEES-97 (Physica B
Semiclassical Theory of Coulomb Blockade Peak Heights in Chaotic Quantum Dots
We develop a semiclassical theory of Coulomb blockade peak heights in chaotic
quantum dots. Using Berry's conjecture, we calculate the peak height
distributions and the correlation functions. We demonstrate that the
corrections to the corresponding results of the standard statistical theory are
non-universal and can be expressed in terms of the classical periodic orbits of
the dot that are well coupled to the leads. The main effect is an oscillatory
dependence of the peak heights on any parameter which is varied; it is
substantial for both symmetric and asymmetric lead placement. Surprisingly,
these dynamical effects do not influence the full distribution of peak heights,
but are clearly seen in the correlation function or power spectrum. For
non-zero temperature, the correlation function obtained theoretically is in
good agreement with that measured experimentally.Comment: 5 color eps figure
Coulomb blockade in metallic grains at large conductance
We study Coulomb blockade effects in the thermodynamic quantities of a weakly
disordered metallic grain coupled to a metallic lead by a tunneling contact
with a large conductance . We consider the case of broken time-reversal
symmetry and obtain expressions for both the {\em ensemble averaged} amplitude
of the Coulomb blockade oscillations of the thermodynamic potential and the
correlator of its {\em mesoscopic fluctuations} for a finite mean level spacing
in the grain. We develop a novel method which allows for an exact
evaluation of the functional integral arising from disorder averaging. The
results and the method are applicable in the temperature range .Comment: 18 pages, 3 figures (revised version
Mesoscopic fluctuations of the Density of States and Conductivity in the middle of the band of Disordered Lattices
The mesoscopic fluctuations of the Density of electronic States (DoS) and of
the conductivity of two- and three- dimensional lattices with randomly
distributed substitutional impurities are studied. Correlations of the levels
lying above (or below) the Fermi surface, in addition to the correlations of
the levels lying on opposite sides of the Fermi surface, take place at half
filling due to nesting. The Bragg reflections mediate to increase static
fluctuations of the conductivity in the middle of the band which change the
distribution function of the conductivity at half- filling.Comment: 5 pages, 3 figure
Critical generalized inverse participation ratio distributions
The system size dependence of the fluctuations in generalized inverse
participation ratios (IPR's) at criticality is investigated
numerically. The variances of the IPR logarithms are found to be
scale-invariant at the macroscopic limit. The finite size corrections to the
variances decay algebraically with nontrivial exponents, which depend on the
Hamiltonian symmetry and the dimensionality. The large- dependence of the
asymptotic values of the variances behaves as according to theoretical
estimates. These results ensure the self-averaging of the corresponding
generalized dimensions.Comment: RevTex4, 5 pages, 4 .eps figures, to be published in Phys. Rev.
Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics
Asymptotical behavior of the distribution function of local density of states
(LDOS) in disordered metallic samples is studied with making use of the
supersymmetric --model approach, in combination with the saddle--point
method. The LDOS distribution is found to have the logarithmically normal
asymptotics for quasi--1D and 2D sample geometry. In the case of a quasi--1D
sample, the result is confirmed by the exact solution. In 2D case a perfect
agreement with an earlier renormalization group calculation is found. In 3D the
found asymptotics is of somewhat different type: P(\rho)\sim
\exp(-\mbox{const}\,|\ln^3\rho|).Comment: REVTEX, 14 pages, no figure
Periodic orbit effects on conductance peak heights in a chaotic quantum dot
We study the effects of short-time classical dynamics on the distribution of
Coulomb blockade peak heights in a chaotic quantum dot. The location of one or
both leads relative to the short unstable orbits, as well as relative to the
symmetry lines, can have large effects on the moments and on the head and tail
of the conductance distribution. We study these effects analytically as a
function of the stability exponent of the orbits involved, and also numerically
using the stadium billiard as a model. The predicted behavior is robust,
depending only on the short-time behavior of the many-body quantum system, and
consequently insensitive to moderate-sized perturbations.Comment: 14 pages, including 6 figure
Diffusion of electrons in random magnetic fields,
Diffusion of electrons in a two-dimensional system in static random magnetic
fields is studied by solving the time-dependent Schr\"{o}dinger equation
numerically. The asymptotic behaviors of the second moment of the wave packets
and the temporal auto-correlation function in such systems are investigated. It
is shown that, in the region away from the band edge, the growth of the
variance of the wave packets turns out to be diffusive, whereas the exponents
for the power-law decay of the temporal auto- correlation function suggest a
kind of fractal structure in the energy spectrum and in the wave functions. The
present results are consistent with the interpretation that the states away
from the band edge region are critical.Comment: 22 pages (8 figures will be mailed if requested), LaTeX, to appear in
Phys. Rev.
Multifractal analysis of the electronic states in the Fibonacci superlattice under weak electric fields
Influence of the weak electric field on the electronic structure of the
Fibonacci superlattice is considered. The electric field produces a nonlinear
dynamics of the energy spectrum of the aperiodic superlattice. Mechanism of the
nonlinearity is explained in terms of energy levels anticrossings. The
multifractal formalism is applied to investigate the effect of weak electric
field on the statistical properties of electronic eigenfunctions. It is shown
that the applied electric field does not remove the multifractal character of
the electronic eigenfunctions, and that the singularity spectrum remains
non-parabolic, however with a modified shape. Changes of the distances between
energy levels of neighbouring eigenstates lead to the changes of the inverse
participation ratio of the corresponding eigenfunctions in the weak electric
field. It is demonstrated, that the local minima of the inverse participation
ratio in the vicinity of the anticrossings correspond to discontinuity of the
first derivative of the difference between marginal values of the singularity
strength. Analysis of the generalized dimension as a function of the electric
field shows that the electric field correlates spatial fluctuations of the
neighbouring electronic eigenfunction amplitudes in the vicinity of
anticrossings, and the nonlinear character of the scaling exponent confirms
multifractality of the corresponding electronic eigenfunctions.Comment: 10 pages, 9 figure