125 research outputs found
Scaling Properties of 1D Anderson Model with Correlated Diagonal Disorder
Statistical and scaling properties of the Lyapunov exponent for a
tight-binding model with the diagonal disorder described by a dichotomic
process are considered near the band edge. The effect of correlations on
scaling properties is discussed. It is shown that correlations lead to an
additional parameter governing the validity of single parameter scaling.Comment: 5 pages, 3 figures, RevTe
Single parameter scaling in 1-D localized absorbing systems
Numerical study of the scaling of transmission fluctuations in the 1-D
localization problem in the presence of absorption is carried out. Violations
of single parameter scaling for lossy systems are found and explained on the
basis of a new criterion for different types of scaling behavior derived by
Deych et al [Phys. Rev. Lett., {\bf 84}, 2678 (2000)].Comment: 7 pages, 6 figures, RevTex, submitted to Phys. Rev.
Spectral engineering with multiple quantum well structures
It is shown that it is possible to significantly modify optical spectra of
Bragg multiple quantum well structures by introducing wells with different
exciton energies. The reflection spectrum of the resulting structures is
characterized by high contrast and tuning possibilities
Effects of spatial non-uniformity on laser dynamics
Semiclassical equations of lasing dynamics are re-derived for a lasing medium
in a cavity with a spatially non-uniform dielectric constant. It is shown that
the non-uniformity causes a radiative coupling between modes of the empty
cavity. This coupling results in a renormalization of self- and
cross-saturation coefficients, which acquire a non-trivial dependence on the
pumping intensity. Possible manifestations of these effects in random lasers
are discussed.Comment: 4 pages, 1 figure, LaTex. Introduction is significantly rewritten,
and the results is placed in the context of random lasin
Need for Undertaking of Strategy for Sustainable Development of Ukraine Which is Baced on Social Responsibility
Обґрунтовано необхідність соціальної відповідальності при реалізації стратегії сталого розвитку в Україні. Розкрито
взаємозв’язок і взаємовплив соціальної відповідальності та сталого розвитку. Запропоновано критерії ефективності виконання стратегії сталого розвитку через модернізацію суспільних відносин на різних рівнях.In the Article is justified need of Social Responsibility during process of realization of Strategy for Sustainable Development of Ukraine. It was explained link between Social Responsibility and Sustainable Development. Also was offered effectiveness measures to ensure compliance with Strategy for Sustainable Development through modernization of social relationships at different levels
Statistics of transmission in one-dimensional disordered systems: universal characteristics of states in the fluctuation tails
We numerically study the distribution function of the conductance
(transmission) in the one-dimensional tight-binding Anderson and
periodic-on-average superlattice models in the region of fluctuation states
where single parameter scaling is not valid. We show that the scaling
properties of the distribution function depend upon the relation between the
system's length and the length determined by the integral density of
states. For long enough systems, , the distribution can still be
described within a new scaling approach based upon the ratio of the
localization length and . In an intermediate interval of the
system's length , , the variance of the Lyapunov
exponent does not follow the predictions of the central limit theorem and this
scaling becomes invalid.Comment: 22 pages, 12 eps figure
Effects of resonant tunneling in electromagnetic wave propagation through a polariton gap
We consider tunneling of electromagnetic waves through a polariton band gap
of a 1-D chain of atoms. We analytically show that a defect embedded in the
structure gives rise to the resonance transmission at the frequency of a local
polariton state associated with the defect. Numerical Monte-Carlo simulations
are used to examine properties of the electromagnetic band arising inside the
polariton gap due to finite concentration of defects.Comment: 12 pages, 6 figures, RevTe
Scaling in the one-dimensional Anderson localization problem in the region of fluctuation states
We numerically study the distribution function of the conductivity
(transmission) in the one-dimensional tight-binding Anderson model in the
region of fluctuation states. We show that while single parameter scaling in
this region is not valid, the distribution can still be described within a
scaling approach based upon the ratio of two fundamental quantities, the
localization length, , and a new length, , related to the
integral density of states. In an intermediate interval of the system's length
, , the variance of the Lyapunov exponent does not
follow the predictions of the central limit theorem, and may even grow with
.Comment: Phys. Rev. Lett 90, 126601 (2003) 4 pages, 3 figure
Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model
We discuss the localization behavior of localized electronic wave functions
in the one- and two-dimensional tight-binding Anderson model with diagonal
disorder. We find that the distributions of the local wave function amplitudes
at fixed distances from the localization center are well approximated by
log-normal fits which become exact at large distances. These fits are
consistent with the standard single parameter scaling theory for the Anderson
model in 1d, but they suggest that a second parameter is required to describe
the scaling behavior of the amplitude fluctuations in 2d. From the log-normal
distributions we calculate analytically the decay of the mean wave functions.
For short distances from the localization center we find stretched exponential
localization ("sublocalization") in both, 1d and 2d. In 1d, for large
distances, the mean wave functions depend on the number of configurations N
used in the averaging procedure and decay faster that exponentially
("superlocalization") converging to simple exponential behavior only in the
asymptotic limit. In 2d, in contrast, the localization length increases
logarithmically with the distance from the localization center and
sublocalization occurs also in the second regime. The N-dependence of the mean
wave functions is weak. The analytical result agrees remarkably well with the
numerical calculations.Comment: 12 pages with 9 figures and 1 tabl
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