339 research outputs found
Metal-insulator transition in three dimensional Anderson model: universal scaling of higher Lyapunov exponents
Numerical studies of the Anderson transition are based on the finite-size
scaling analysis of the smallest positive Lyapunov exponent. We prove
numerically that the same scaling holds also for higher Lyapunov exponents.
This scaling supports the hypothesis of the one-parameter scaling of the
conductance distribution. From the collected numerical data for quasi one
dimensional systems up to the system size 24 x 24 x infinity we found the
critical disorder 16.50 < Wc < 16.53 and the critical exponent 1.50 < \nu <
1.54. Finite-size effects and the role of irrelevant scaling parameters are
discussed.Comment: 4 pages, 2 figure
Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial
Light propagation through 1D disordered structures composed of alternating
layers, with random thicknesses, of air and a dispersive metamaterial is
theoretically investigated. Both normal and oblique incidences are considered.
By means of numerical simulations and an analytical theory, we have established
that Anderson localization of light may be suppressed: (i) in the long
wavelength limit, for a finite angle of incidence which depends on the
parameters of the dispersive metamaterial; (ii) for isolated frequencies and
for specific angles of incidence, corresponding to Brewster anomalies in both
positive- and negative-refraction regimes of the dispersive metamaterial. These
results suggest that Anderson localization of light could be explored to
control and tune light propagation in disordered metamaterials.Comment: 4 two-column pages, 3 figure
Finite-size scaling from self-consistent theory of localization
Accepting validity of self-consistent theory of localization by Vollhardt and
Woelfle, we derive the finite-size scaling procedure used for studies of the
critical behavior in d-dimensional case and based on the use of auxiliary
quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good
agreement with numerical results: it signifies the absence of essential
contradictions with the Vollhardt and Woelfle theory on the level of raw data.
The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of
the correlation length, are explained by the fact that dependence L+L_0 with
L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu}
with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived;
it demonstrates incorrectness of the conventional treatment of data for d=4 and
d=5, but establishes the constructive procedure for such a treatment.
Consequences for other variants of finite-size scaling are discussed.Comment: Latex, 23 pages, figures included; additional Fig.8 is added with
high precision data by Kramer et a
Topology dependent quantities at the Anderson transition
The boundary condition dependence of the critical behavior for the three
dimensional Anderson transition is investigated. A strong dependence of the
scaling function and the critical conductance distribution on the boundary
conditions is found, while the critical disorder and critical exponent are
found to be independent of the boundary conditions
Anderson localization of light in disordered superlattices containing graphene layers
We theoretically investigate light propagation and Anderson localization in
one-dimensional disordered superlattices composed of dielectric stacks with
graphene sheets in between. Disorder is introduced either on graphene material
parameters ({\it e.g.} Fermi energy) or on the widths of the dielectric stacks.
We derive an analytic expression for the localization length , and compare
it to numerical simulations using transfer matrix technique; a very good
agreement is found. We demonstrate that the presence of graphene may strongly
attenuate the anomalously delocalised Breswter modes, and is at the origin of a
periodic dependence of on frequency, in contrast to the usual asymptotic
decay, . By unveiling the effects of graphene on
Anderson localization of light, we pave the way for new applications of
graphene-based, disordered photonic devices in the THz spectral range.We thank W. Kort-Kamp for useful discussions. A.
J. Chaves acknowledge the scholarship from the Brazilian
agency CNPq (Conselho Nacional de Desenvolvimento
Científico e Tecnológico). N.M.R.P. acknowledges financial
support from the Graphene Flagship Project (Contract No.
CNECT-ICT-604391). F.A.P. thanks the Optoelectronics Research Centre and Centre for Photonic Metamaterials, University
of Southampton, for the hospitality, and CAPES for
funding his visit (Grant No. BEX 1497/14-6). F.A.P. also acknowledges
CNPq (Grant No. 303286/2013-0) for financial
support
Localization and Absorption of Light in 2D Composite Metal-Dielectric Films at the Percolation Threshold
We study in this paper the localization of light and the dielectric
properties of thin metal-dielectric composites at the percolation threshold and
around a resonant frequency where the conductivities of the two components are
of the same order. In particular, the effect of the loss in metallic components
are examined. To this end, such systems are modelized as random networks,
and the local field distribution as well as the effective conductivity are
determined by using two different methods for comparison: an exact resolution
of Kirchoff equations, and a real space renormalization group method. The
latter method is found to give the general behavior of the effective
conductivity but fails to determine the local field distribution. It is also
found that the localization still persists for vanishing losses. This result
seems to be in agreement with the anomalous absorption observed experimentally
for such systems.Comment: 14 page latex, 3 ps figures. submitte
Fokker-Planck description of the transfer matrix limiting distribution in the scattering approach to quantum transport
The scattering approach to quantum transport through a disordered
quasi-one-dimensional conductor in the insulating regime is discussed in terms
of its transfer matrix \bbox{T}. A model of one-dimensional wires which
are coupled by random hopping matrix elements is compared with the transfer
matrix model of Mello and Tomsovic. We derive and discuss the complete
Fokker-Planck equation which describes the evolution of the probability
distribution of \bbox{TT}^{\dagger} with system length in the insulating
regime. It is demonstrated that the eigenvalues of \ln\bbox{TT}^{\dagger}
have a multivariate Gaussian limiting probability distribution. The parameters
of the distribution are expressed in terms of averages over the stationary
distribution of the eigenvectors of \bbox{TT}^{\dagger}. We compare the
general form of the limiting distribution with results of random matrix theory
and the Dorokhov-Mello-Pereyra-Kumar equation.Comment: 25 pages, revtex, no figure
Exploring the structure of the quenched QCD vacuum with overlap fermions
Overlap fermions have an exact chiral symmetry on the lattice and are thus an
appropriate tool for investigating the chiral and topological structure of the
QCD vacuum. We study various chiral and topological aspects of quenched gauge
field configurations. This includes the localization and chiral properties of
the eigenmodes, the local structure of the ultraviolet filtered field strength
tensor, as well as the structure of topological charge fluctuations. We
conclude that the vacuum has a multifractal structure.Comment: 68 pages, 31 figures, file size: 1.7 MB (PDF
Dilatation in the femoral vascular bed does not cause retrograde relaxation of the iliac artery in the anaesthetized pig
Aim: We tested the hypothesis that dilatation of a feeding artery may be elicited by transmission of a signal through the tissue of the arterial wall from a vasodilated peripheral vascular bed. Methods: In eight pentobarbital anaesthetized pigs, acetylcholine (ACh, an endothelium-dependent vasodilator) was injected intra-arterially above (upstream) and below (downstream) a test segment of the left iliac artery, the diameter of which was measured continuously by sonomicrometry. Results: Under control conditions, ACh injections upstream and downstream of the test segment caused dilatation. Downstream injection dilated the peripheral arterioles, resulting in increased blood flow and proximal dilatation. This is a shear stress, nitric oxide (NO)-dependent response. The experiment was then repeated after applying a stenosis to prevent the increased flow caused by downstream injection of ACh; the stenosis was placed either above the site of diameter measurement to allow retrograde conduction, or below that site to prevent distally injected ACh reaching the measurement site. Under these conditions, downstream injection of ACh had a minimal effect on the shear stress of the test segment with no increase in test segment diameter. This was not due to endothelial damage or dysfunction as injection of ACh upstream still caused a large increase in test segment diameter. Conclusions: Our results indicate that dilatation of the feeding artery of a vasodilated bed is caused by increased shear stress within the feeding artery and not via a signal transmitted through the arterial wall from below
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