391 research outputs found
What is the right theory for Anderson localization of light?
Anderson localization of light is traditionally described in analogy to
electrons in a random potential. Within this description the disorder strength
-- and hence the localization characteristics -- depends strongly on the
wavelength of the incident light. In an alternative description in analogy to
sound waves in a material with spatially fluctuating elastic moduli this is not
the case. Here, we report on an experimentum crucis in order to investigate the
validity of the two conflicting theories using transverse-localized optical
devices. We do not find any dependence of the observed localization radii on
the light wavelength. We conclude that the modulus-type description is the
correct one and not the potential-type one. We corroborate this by showing that
in the derivation of the traditional, potential-type theory a term in the wave
equation has been tacititly neglected. In our new modulus-type theory the wave
equation is exact. We check the consistency of the new theory with our data
using a field-theoretical approach (nonlinear sigma model)
Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"
We consider a system of coupled classical harmonic oscillators with spatially
fluctuating nearest-neighbor force constants on a simple cubic lattice. The
model is solved both by numerically diagonalizing the Hamiltonian and by
applying the single-bond coherent potential approximation. The results for the
density of states are in excellent agreement with each other. As
the degree of disorder is increased the system becomes unstable due to the
presence of negative force constants. If the system is near the borderline of
stability a low-frequency peak appears in the reduced density of states
as a precursor of the instability. We argue that this peak
is the analogon of the "boson peak", observed in structural glasses. By means
of the level distance statistics we show that the peak is not associated with
localized states
The evolution of vibrational excitations in glassy systems
The equations of the mode-coupling theory (MCT) for ideal liquid-glass
transitions are used for a discussion of the evolution of the
density-fluctuation spectra of glass-forming systems for frequencies within the
dynamical window between the band of high-frequency motion and the band of
low-frequency-structural-relaxation processes. It is shown that the strong
interaction between density fluctuations with microscopic wave length and the
arrested glass structure causes an anomalous-oscillation peak, which exhibits
the properties of the so-called boson peak. It produces an elastic modulus
which governs the hybridization of density fluctuations of mesoscopic wave
length with the boson-peak oscillations. This leads to the existence of
high-frequency sound with properties as found by X-ray-scattering spectroscopy
of glasses and glassy liquids. The results of the theory are demonstrated for a
model of the hard-sphere system. It is also derived that certain schematic MCT
models, whose spectra for the stiff-glass states can be expressed by elementary
formulas, provide reasonable approximations for the solutions of the general
MCT equations.Comment: 50 pages, 17 postscript files including 18 figures, to be published
in Phys. Rev.
On the high-density expansion for Euclidean Random Matrices
Diagrammatic techniques to compute perturbatively the spectral properties of
Euclidean Random Matrices in the high-density regime are introduced and
discussed in detail. Such techniques are developed in two alternative and very
different formulations of the mathematical problem and are shown to give
identical results up to second order in the perturbative expansion. One method,
based on writing the so-called resolvent function as a Taylor series, allows to
group the diagrams in a small number of topological classes, providing a simple
way to determine the infrared (small momenta) behavior of the theory up to
third order, which is of interest for the comparison with experiments. The
other method, which reformulates the problem as a field theory, can instead be
used to study the infrared behaviour at any perturbative order.Comment: 29 page
Giant negative magnetoresistance in semiconductors doped by multiply charged deep impurities
A giant negative magnetoresistance has been observed in bulk germanium doped
with multiply charged deep impurities. Applying a magnetic field the resistance
may decrease exponentially at any orientation of the field. A drop of the
resistance as much as about 10000% has been measured at 6 T. The effect is
attributed to the spin splitting of impurity ground state with a very large
g-factor in the order of several tens depending on impurity.Comment: 4 pages, 4 figure
Physical Origin of the Boson Peak Deduced from a Two-Order-Parameter Model of Liquid
We propose that the boson peak originates from the (quasi-) localized
vibrational modes associated with long-lived locally favored structures, which
are intrinsic to a liquid state and are randomly distributed in a sea of
normal-liquid structures. This tells us that the number density of locally
favored structures is an important physical factor determining the intensity of
the boson peak. In our two-order-parameter model of the liquid-glass
transition, the locally favored structures act as impurities disturbing
crystallization and thus lead to vitrification. This naturally explains the
dependence of the intensity of the boson peak on temperature, pressure, and
fragility, and also the close correlation between the boson peak and the first
sharp diffraction peak (or prepeak).Comment: 5 pages, 1 figure, An error in the reference (Ref. 7) was correcte
Voronoi-Delaunay analysis of normal modes in a simple model glass
We combine a conventional harmonic analysis of vibrations in a one-atomic
model glass of soft spheres with a Voronoi-Delaunay geometrical analysis of the
structure. ``Structure potentials'' (tetragonality, sphericity or perfectness)
are introduced to describe the shape of the local atomic configurations
(Delaunay simplices) as function of the atomic coordinates. Apart from the
highest and lowest frequencies the amplitude weighted ``structure potential''
varies only little with frequency. The movement of atoms in soft modes causes
transitions between different ``perfect'' realizations of local structure. As
for the potential energy a dynamic matrix can be defined for the ``structure
potential''. Its expectation value with respect to the vibrational modes
increases nearly linearly with frequency and shows a clear indication of the
boson peak. The structure eigenvectors of this dynamical matrix are strongly
correlated to the vibrational ones. Four subgroups of modes can be
distinguished
Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations
The approach of the elastic continuum limit in small amorphous bodies formed
by weakly polydisperse Lennard-Jones beads is investigated in a systematic
finite-size study. We show that classical continuum elasticity breaks down when
the wavelength of the sollicitation is smaller than a characteristic length of
approximately 30 molecular sizes. Due to this surprisingly large effect
ensembles containing up to N=40,000 particles have been required in two
dimensions to yield a convincing match with the classical continuum predictions
for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk
systems. The existence of an effective length scale \xi is confirmed by the
analysis of the (non-gaussian) noisy part of the low frequency vibrational
eigenmodes. Moreover, we relate it to the {\em non-affine} part of the
displacement fields under imposed elongation and shear. Similar correlations
(vortices) are indeed observed on distances up to \xi~30 particle sizes.Comment: 28 pages, 13 figures, 3 table
Hopping Transport in the Presence of Site Energy Disorder: Temperature and Concentration Scaling of Conductivity Spectra
Recent measurements on ion conducting glasses have revealed that conductivity
spectra for various temperatures and ionic concentrations can be superimposed
onto a common master curve by an appropriate rescaling of the conductivity and
frequency. In order to understand the origin of the observed scaling behavior,
we investigate by Monte Carlo simulations the diffusion of particles in a
lattice with site energy disorder for a wide range of both temperatures and
concentrations. While the model can account for the changes in ionic activation
energies upon changing the concentration, it in general yields conductivity
spectra that exhibit no scaling behavior. However, for typical concentrations
and sufficiently low temperatures, a fairly good data collapse is obtained
analogous to that found in experiment.Comment: 6 pages, 4 figure
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