97,142 research outputs found
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.
Probing magnetic turbulence by synchrotron polarimetry: statistics and structure of magnetic fields from Stokes correlators
We describe a technique for probing the statistical properties of cosmic
magnetic fields based on radio polarimetry data. Second-order magnetic field
statistics like the power spectrum cannot always distinguish between magnetic
fields with essentially different spatial structure. Synchrotron polarimetry
naturally allows certain 4th-order magnetic field statistics to be inferred
from observational data, which lifts this degeneracy and can thereby help us
gain a better picture of the structure of the cosmic fields and test
theoretical scenarios describing magnetic turbulence. In this work we show that
a 4th-order correlator of physical interest, the tension-force spectrum, can be
recovered from the polarized synchrotron emission data. We develop an estimator
for this quantity based on polarized-emission observations in the
Faraday-rotation-free frequency regime. We consider two cases: a statistically
isotropic field distribution, and a statistically isotropic field superimposed
on a weak mean field. In both cases the tension force power spectrum is
measurable; in the latter case, the magnetic power spectrum may also be
obtainable. The method is exact in the idealized case of a homogeneous
relativistic-electron distribution that has a power-law energy spectrum with a
spectral index p=3, and assumes statistical isotropy of the turbulent field. We
carry out tests of our method using synthetic data generated from numerically
simulated magnetic fields. We show that the method is valid, that it is not
prohibitively sensitive to the value of the electron spectral index, and that
the observed tension-force spectrum allows one to distinguish between, e.g., a
randomly tangled magnetic field (a default assumption in many studies) and a
field organized in folded flux sheets or filaments.Comment: Published on MNRAS 200
A Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguides
This works deals with one dimensional infinite perturbation - namely line
defects - in periodic media. In optics, such defects are created to construct
an (open) waveguide that concentrates light. The existence and the computation
of the eigenmodes is a crucial issue. This is related to a self-adjoint
eigenvalue problem associated to a PDE in an unbounded domain (in the
directions orthogonal to the line defect), which makes both the analysis and
the computations more complex. Using a Dirichlet-to-Neumann (DtN) approach, we
show that this problem is equivalent to one set on a small neighborhood of the
defect. On contrary to existing methods, this one is exact but there is a price
to be paid : the reduction of the problem leads to a nonlinear eigenvalue
problem of a fixed point nature
The Hopf structure of some dual operator algebras
We study the Hopf structure of a class of dual operator algebras
corresponding to certain semigroups. This class of algebras arises in dilation
theory, and includes the noncommutative analytic Toeplitz algebra and the
multiplier algebra of the Drury-Arveson space, which correspond to the free
semigroup and the free commutative semigroup respectively. The preduals of the
algebras in this class naturally form Hopf (convolution) algebras. The original
algebras and their preduals form (non-self-adjoint) dual Hopf algebras in the
sense of Effros and Ruan. We study these algebras from this perspective, and
obtain a number of results about their structure.Comment: 30 page
Multi-particle structure in the Z_n-chiral Potts models
We calculate the lowest translationally invariant levels of the Z_3- and
Z_4-symmetrical chiral Potts quantum chains, using numerical diagonalization of
the hamiltonian for N <= 12 and N <= 10 sites, respectively, and extrapolating
N to infinity. In the high-temperature massive phase we find that the pattern
of the low-lying zero momentum levels can be explained assuming the existence
of n-1 particles carrying Z_n-charges Q = 1, ... , n-1 (mass m_Q), and their
scattering states. In the superintegrable case the masses of the n-1 particles
become proportional to their respective charges: m_Q = Q m_1. Exponential
convergence in N is observed for the single particle gaps, while power
convergence is seen for the scattering levels. We also verify that
qualitatively the same pattern appears for the self-dual and integrable cases.
For general Z_n we show that the energy-momentum relations of the particles
show a parity non-conservation asymmetry which for very high temperatures is
exclusive due to the presence of a macroscopic momentum P_m=(1-2Q/n)/\phi,
where \phi is the chiral angle and Q is the Z_n-charge of the respective
particle.Comment: 22 pages (LaTeX) plus 5 figures (included as PostScript),
BONN-HE-92-3
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