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 $L$ and the length $l_s$ determined by the integral density of states. For long enough systems, $L \gg l_s$, the distribution can still be described within a new scaling approach based upon the ratio of the localization length $l_{loc}$ and $l_s$. In an intermediate interval of the system's length $L$, $l_{loc}\ll L\ll l_s$, 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, $l_{loc}$, and a new length, $l_s$, related to the integral density of states. In an intermediate interval of the system's length $L$, $l_{loc}\ll L\ll l_s$, the variance of the Lyapunov exponent does not follow the predictions of the central limit theorem, and may even grow with $L$.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