55 research outputs found
Non-analyticity in the distribution of conductances in quasi one dimensional wires
We show that the distribution P(g) of conductances g of a quasi one
dimensional wire has non-analytic behavior in the insulating region, leading to
a discontinuous derivative in the distribution near g=1. We give analytic
expressions for the full distribution and extract an approximate scaling
behavior valid for different strengths of disorder close to g=1.Comment: 7 pages, 3 figures. Submitted to Europhysics Letter
Statistical analysis of the transmission based on the DMPK equation: An application to Pb nano-contacts
The density of the transmission eigenvalues of Pb nano-contacts has been
estimated recently in mechanically controllable break-junction experiments.
Motivated by these experimental analyses, here we study the evolution of the
density of the transmission eigenvalues with the disorder strength and the
number of channels supported by the ballistic constriction of a quantum point
contact in the framework of the Dorokhov-Mello-Pereyra-Kumar equation. We find
that the transmission density evolves rapidly into the density in the diffusive
metallic regime as the number of channels of the constriction increase.
Therefore, the transmission density distribution for a few channels comes
close to the known bimodal density distribution in the metallic limit. This is
in agreement with the experimental statistical-studies in Pb nano-contacts. For
the two analyzed cases, we show that the experimental densities are seen to be
well described by the corresponding theoretical results.Comment: 6 pages, 6 figure
A Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems
We perform a detailed numerical study of the conductance through
one-dimensional (1D) tight-binding wires with on-site disorder. The random
configurations of the on-site energies of the tight-binding
Hamiltonian are characterized by long-tailed distributions: For large
, with . Our
model serves as a generalization of 1D Lloyd's model, which corresponds to
. First, we verify that the ensemble average is proportional to the length of the wire for all values of
, providing the localization length from . Then, we show that the probability distribution
function is fully determined by the exponent and
. In contrast to 1D wires with standard
white-noise disorder, our wire model exhibits bimodal distributions of the
conductance with peaks at and . In addition, we show that
is proportional to , for , with , in
agreement to previous studies.Comment: 5 pages, 5 figure
Photonic heterostructures with Levy-type disorder: statistics of coherent transmission
We study the electromagnetic transmission through one-dimensional (1D)
photonic heterostructures whose random layer thicknesses follow a long-tailed
distribution --L\'evy-type distribution. Based on recent predictions made for
1D coherent transport with L\'evy-type disorder, we show numerically that for a
system of length (i) the average for
for , being the
exponent of the power-law decay of the layer-thickness probability
distribution; and (ii) the transmission distribution is independent of
the angle of incidence and frequency of the electromagnetic wave, but it is
fully determined by the values of and .Comment: 4 pages, 4 figure
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
Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption
We are interested in finding the joint distribution function of the real and
imaginary parts of the local Green function for a system with chaotic internal
wave scattering and a uniform energy loss (absorption). For a microwave cavity
attached to a single-mode antenna the same quantity has a meaning of the
complex cavity impedance. Using the random matrix approach, we relate its
statistics to that of the reflection coefficient and scattering phase and
provide exact distributions for systems with beta=2 and beta=4 symmetry class.
In the case of beta=1 we provide an interpolation formula which incorporates
all known limiting cases and fits excellently available experimental data as
well as diverse numeric tests.Comment: 4 pages, 1 figur
Delay time of waves performing Levy walks in 1D random media
[EN] The time that waves spend inside 1D random media with the possibility of performing Lévy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered systems via the delay time. We show that a wide class of disorder¿Lévy disorder¿leads to strong random fluctuations of the delay time; nevertheless, some statistical properties such as the tail of the distribution and the average of the delay time are insensitive to Lévy walks. Our results reveal a universal character of wave propagation that goes beyond standard Brownian wave-diffusion.A. A. F.-M. thanks the hospitality of the Laboratoire d'Acoustique de l'Universite du Mans, France, where part of this work was done. J. A. M.-B, gratefully acknowledges to Departamento de Matematica Aplicada e Estatistica, Instituto de Ciencias Matematicas e de Computacao, Universidade de Sao Paulo during which this work was completed. J.A.M.-B. was supported by FAPESP (Grant No. 2019/06931-2), Brazil. A. A. F.-M. thanks partial support by RFI Le Mans Acoustique and by the project HYPERMETA funded under the program Etoiles Montantes of the Region Pays de la Loire. V. A. G. acknowledges support by MCIU (Spain) under the Project number PGC2018-094684-B-C22.Razo-López, LA.; Fernández-Marín, AA.; Mendez-Bermudez, JA.; Sánchez-Dehesa Moreno-Cid, J.; Gopar, VA. (2020). Delay time of waves performing Levy walks in 1D random media. Scientific Reports. 10(1):1-8. https://doi.org/10.1038/s41598-020-77861-xS18101Wigner, E. P. Lower limit for the energy derivative of the scattering phase shift. Phys. Rev. 147, 145–147 (1955).Smith, F. T. Lifetime matrix in collision theory. Phys. Rev. 119, 2098–2098 (1960).Fercher, A. F., Drexler, W., Hitzenberger, C. K. & Lasser, T. Optical coherence tomography -principles and applications. Rep. Prog. Phys. 66, 239–303 (2003).Lubatsch, A. & Frank, R. 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Universality of the Wigner time delay distribution for one-dimensional random potentials
We show that the distribution of the time delay for one-dimensional random
potentials is universal in the high energy or weak disorder limit. Our
analytical results are in excellent agreement with extensive numerical
simulations carried out on samples whose sizes are large compared to the
localisation length (localised regime). The case of small samples is also
discussed (ballistic regime). We provide a physical argument which explains in
a quantitative way the origin of the exponential divergence of the moments. The
occurence of a log-normal tail for finite size systems is analysed. Finally, we
present exact results in the low energy limit which clearly show a departure
from the universal behaviour.Comment: 4 pages, 3 PostScript figure
Statistics of Dynamics of Localized Waves
The measured distribution of the single-channel delay time of localized
microwave radiation and its correlation with intensity differ sharply from the
behavior of diffusive waves. The delay time is found to increase with
intensity, while its variance is inversely proportional to the fourth root of
the intensity. The distribution of the delay time weighted by the intensity is
found to be a double-sided stretched exponential to the 1/3 power centered at
zero. The correlation between dwell time and intensity provides a dynamical
test of photon localization.Comment: submitted to PRL; 4 pages including 6 figure
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