13 research outputs found
Coherent wave transmission in quasi-one-dimensional systems with L\'evy disorder
We study the random fluctuations of the transmission in disordered
quasi-one-dimensional systems such as disordered waveguides and/or quantum
wires whose random configurations of disorder are characterized by density
distributions with a long tail known as L\'evy distributions. The presence of
L\'evy disorder leads to large fluctuations of the transmission and anomalous
localization, in relation to the standard exponential localization (Anderson
localization). We calculate the complete distribution of the transmission
fluctuations for different number of transmission channels in the presence and
absence of time-reversal symmetry. Significant differences in the transmission
statistics between disordered systems with Anderson and anomalous localizations
are revealed. The theoretical predictions are independently confirmed by tight
binding numerical simulations.Comment: 10 pages, 6 figure
Statistical study of the conductance and shot noise in open quantum-chaotic cavities: Contribution from whispering gallery modes
In the past, a maximum-entropy model was introduced and applied to the study
of statistical scattering by chaotic cavities, when short paths may play an
important role in the scattering process. In particular, the validity of the
model was investigated in relation with the statistical properties of the
conductance in open chaotic cavities. In this article we investigate further
the validity of the maximum-entropy model, by comparing the theoretical
predictions with the results of computer simulations, in which the Schroedinger
equation is solved numerically inside the cavity for one and two open channels
in the leads; we analyze, in addition to the conductance, the zero-frequency
limit of the shot-noise power spectrum. We also obtain theoretical results for
the ensemble average of this last quantity, for the orthogonal and unitary
cases of the circular ensemble and an arbitrary number of channels. Generally
speaking, the agreement between theory and numerics is good. In some of the
cavities that we study, short paths consist of whispering gallery modes, which
were excluded in previous studies. These cavities turn out to be all the more
interesting, as it is in relation with them that we found certain systematic
discrepancies in the comparison with theory. We give evidence that it is the
lack of stationarity inside the energy interval that is analyzed, and hence the
lack of ergodicity that gives rise to the discrepancies. Indeed, the agreement
between theory and numerical simulations is improved when the energy interval
is reduced to a point and the statistics is then collected over an ensemble. It
thus appears that the maximum-entropy model is valid beyond the domain where it
was originally derived. An understanding of this situation is still lacking at
the present moment.Comment: Revised version, minor modifications, 28 pages, 7 figure
The invariant measure for scattering matrices with block symmetries
Abstract. We find the invariant measure for two new types of S matrices relevant for chaotic scattering from a cavity in a waveguide. The S matrices considered can be written as a 2 × 2 matrix of blocks, each of rank N, in which the two diagonal blocks are identical and the two off-diagonal blocks are identical. The S matrices are unitary; in addition, they may be symmetric because of time-reversal symmetry. The invariant measure, with and without the condition of symmetry, is given explicitly in terms of the invariant measures for the well known circular unitary and orthogonal ensembles. Some implications are drawn for the resulting statistical distribution of the transmission coefficient through a chaotic cavity
Conductance of 1D quantum wires with anomalous electron-wavefunction localization
We study the statistics of the conductance through one-dimensional
disordered systems where electron wavefunctions decay spatially as for , being a constant. In
contrast to the conventional Anderson localization where and the conductance statistics is determined by a single
parameter: the mean free path, here we show that when the wave function is
anomalously localized () the full statistics of the conductance is
determined by the average and the power . Our theoretical
predictions are verified numerically by using a random hopping tight-binding
model at zero energy, where due to the presence of chiral symmetry in the
lattice there exists anomalous localization; this case corresponds to the
particular value . To test our theory for other values of
, we introduce a statistical model for the random hopping in the tight
binding Hamiltonian.Comment: 6 pages, 8 figures. Few changes in the presentation and references
updated. Published in PRB, Phys. Rev. B 85, 235450 (2012
Conductance distribution in disordered quantum wires: Crossover between the metallic and insulating regimes
We calculate the distribution of the conductance P(g) for a
quasi-one-dimensional system in the metal to insulator crossover regime, based
on a recent analytical method valid for all strengths of disorder. We show the
evolution of P(g) as a function of the disorder parameter from a insulator to a
metal. Our results agree with numerical studies reported on this problem, and
with analytical results for the average and variance of g.Comment: 8 pages, 5 figures. Final version (minor changes
Orbital entanglement and electron localization in quantum wires
We study the signatures of disorder in the production of orbital electron
entanglement in quantum wires. Disordered entanglers suffer the effects of
localization of the electron wave function and random fluctuations in the
entanglement production. This manifests in the statistics of the concurrence, a
measure of the produced two-qubit entanglement. We calculate the concurrence
distribution as a function of the disorder strength within a random-matrix
approach. We also identify significant constraints on the entanglement
production as a consequence of the breaking/preservation of time-reversal
invariance. Additionally, our theoretical results are independently supported
by simulations of disordered quantum wires based on a tight-binding model.Comment: 6 pages, 4 figures. Minor change
Mesoscopic Capacitors: A Statistical Analysis
The capacitance of mesoscopic samples depends on their geometry and physical
properties, described in terms of characteristic times scales. The resulting ac
admittance shows sample to sample fluctuations. Their distribution is studied
here -through a random-matrix model- for a chaotic cavity capacitively coupled
to a backgate: it is observed from the distribution of scattering time delays
for the cavity, which is found analytically for the orthogonal, unitary, and
symplectic universality classes, one mode in the lead connecting the cavity to
the reservoir and no direct scattering. The results agree with numerical
simulations.Comment: 4 pages (Revtex), 4 PS figures. Minor corrections. New e-mail
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