76,018 research outputs found
Mesoscopic non-equilibrium thermodynamics approach to non-Debye dielectric relaxation
Mesoscopic non-equilibrium thermodynamics is used to formulate a model
describing non-homogeneous and non-Debye dielectric relaxation. The model is
presented in terms of a Fokker-Planck equation for the probability distribution
of non-interacting polar molecules in contact with a heat bath and in the
presence of an external time-dependent electric field. Memory effects are
introduced in the Fokker-Planck description through integral relations
containing memory kernels, which in turn are used to establish a connection
with fractional Fokker-Planck descriptions. The model is developed in terms of
the evolution equations for the first two moments of the distribution function.
These equations are solved by following a perturbative method from which the
expressions for the complex susceptibilities are obtained as a functions of the
frequency and the wave number. Different memory kernels are considered and used
to compare with experiments of dielectric relaxation in glassy systems. For the
case of Cole-Cole relaxation, we infer the distribution of relaxation times and
its relation with an effective distribution of dipolar moments that can be
attributed to different segmental motions of the polymer chains in a melt.Comment: 33 pages, 6 figure
Statistical determination of the length dependence of high-order polarization mode dispersion
We describe a method of characterizing high-order polarization mode dispersion (PMD).Using a new expansion to approximate the Jones matrix of a polarization-dispersive medium, we study the length dependence of high-order PMD to the fourth order. A simple rule for the asymptotic behavior of PMD for short and long fibers is found. It is also shown that, in long fibers (~1000 km), at 40 Gbits/s the third- and fourth-order PMD may become comparable to the second-order PMD
Stretched exponential relaxation and ac universality in disordered dielectrics
This paper is concerned with the connection between the properties of
dielectric relaxation and ac (alternating-current) conduction in disordered
dielectrics. The discussion is divided between the classical linear-response
theory and a self-consistent dynamical modeling. The key issues are, stretched
exponential character of dielectric relaxation, power-law power spectral
density, and anomalous dependence of ac conduction coefficient on frequency. We
propose a self-consistent model of dielectric relaxation, in which the
relaxations are described by a stretched exponential decay function.
Mathematically, our study refers to the expanding area of fractional calculus
and we propose a systematic derivation of the fractional relaxation and
fractional diffusion equations from the property of ac universality.Comment: 8 pages, 2 figure
Statistical switching kinetics in ferroelectrics
By assuming a more realistic nucleation and polarization reversal scenario we
build a new statistical switching model for ferroelectrics, which is different
from either the Kolmogorov-Avrami-Ishibashi (KAI) model or the
Nucleation-Limited-Switching (NLS) model. After incorporating a time-dependent
depolarization field this model gives a good description about the retardation
behavior in polycrystalline thin films at medium or low fields, which can not
be described by the traditional KAI model. This model predicts correctly n=1
for polycrystalline thin films at high Eappl or ceramic bulks in the ideal
case
Exact Model for Mode-Dependent Gains and Losses in Multimode Fiber
In the strong mode coupling regime, the model for mode-dependent gains and
losses (collectively referred as MDL) of a multimode fiber is extended to the
region with large MDL. The MDL is found to have the same statistical properties
as the eigenvalues of the summation of two matrices. The first matrix is a
random Gaussian matrix with standard deviation proportional to the accumulated
MDL. The other matrix is a deterministic matrix with uniform eigenvalues
proportional to the square of the accumulated MDL. The results are analytically
correct for fibers with two or large number of modes, and also numerically
verified for other cases.Comment: 7 pages, 2 figures, 2 table
Solutions to the dynamical equation of polarization-mode dispersion and polarization-dependent losses
We study the evolution of optical signals in single-mode optical fibers in the presence of polarization-mode dispersion and polarization-dependent losses. Two geometric vectors on the Poincare sphere are defined to characterize the effects of polarization-mode dispersion and polarization-dependent losses on the optical field in the fiber. By solving the dynamical equation for these two vectors, several general statistical results are obtained. The practically important weak polarization-dependent-loss situation is discussed in detail
Electron spin relaxation by nuclei in semiconductor quantum dots
We have studied theoretically the electron spin relaxation in semiconductor
quantum dots via interaction with nuclear spins. The relaxation is shown to be
determined by three processes: (i) -- the precession of the electron spin in
the hyperfine field of the frozen fluctuation of the nuclear spins; (ii) -- the
precession of the nuclear spins in the hyperfine field of the electron; and
(iii) -- the precession of the nuclear spin in the dipole field of its nuclear
neighbors. In external magnetic fields the relaxation of electron spins
directed along the magnetic field is suppressed. Electron spins directed
transverse to the magnetic field relax completely in a time on the order of the
precession period of its spin in the field of the frozen fluctuation of the
nuclear spins. Comparison with experiment shows that the hyperfine interaction
with nuclei may be the dominant mechanism of electron spin relaxation in
quantum dots
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