Solitons in a disordered anisotropic optical medium

The radiation-mediated interaction of solitons in a one-dimensional nonlinear medium (optical fiber) with birefringent disorder is shown to be independent of the separation between solitons. The effect produces a potentially dangerous contribution to the signal lost.     

Nonuniform elastomagnetoelectric effects in a disordered medium

A system of nonlinear equations for the determination of the ground state and the analysis of the possibility of the existence of different elastomagnetoelectric effects in the presence of nonuniform external influences has been obtained by the method of variation of the thermodynamic potential of the disordered medium over the electric and magnetic field strengths and elastic strains. It has been shown that the nonuniform strains created by the gravitational or centrifugal forces can serve as a source of the internal electric fields.     

Diffusion of circularly polarized light in a disordered medium with large-scale inhomogeneities

It is shown that in the presence of diffusion of electromagnetic waves in random media containing large discrete scatterers, circular polarization can persist even after the radiation flux is isotropized. For scattering exactly in the backward direction, this effect is manifested as an increase in the interference contribution to the cross-polarized component of the intensity as the size of the scatterers increases. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 21–26 (10 July 1998)     

Particle transport in a disordered medium: Numerical experiment

Using the multicenter Schrödinger equation for calculating the transmittance of a flat layer of randomly distributed point scattering centers through which a particle passes, we show that when the scattering length for one center is comparable to the particle wavelength λ or is larger, the Ioffe-Regel hypothesis holds. (According to this hypothesis, as the scatterer number density increases, the transmittance of the layer becomes constant, while the value of the particle’s effective mean free path remains of order λ.) When the scattering length is small compared to λ, the Ioffe-Regel hypothesis does not hold. As the scattering length decreases, the accuracy of the approximation of the effective scattering potential gradually increases, and, depending on the strength of the potential, particles may either tunnel or diffuse; the effective mean free path can be much smaller than λ.     

Sample-to-sample fluctuations in the conductivity of a disordered medium

We investigate the sample-to-sample fluctuations in the conductivity of a random resistor network—equivalently, in the diffusivity of a disordered medium with symmetric hopping rates. We argue that whenever the effective conductivity ^* is strictly positive, then the fluctuations are normal, i.e., proportional to (volume)^–1/2. If the local conductivities are allowed to be zero, then ^* vanishes when approaching the percolation thresholdp _c. Close top _c the fluctuations are anomalous. From the renormalization group on hierarchical lattices we find that atp _c fluctuations and mean scale in the same fashion, i.e., there is no independent scaling exponent for the fluctuations.     

High-frequency dielectric constant of a two-dimensionally disordered model medium

An exact solution is derived for the two-dimensional two-phase model of a disordered medium proposed by Morozovskii and Snarskii [Ukr. Fiz. Zh. (Russ. Ed.) 28, 1230 (1983)] that arises because of hierarchical mixing of phases with different dielectric constants. The problem reduces to a nonlinear recurrence relation for the dielectric constants. It is found that the expressions for the dielectric constants at the nth stage of the iteration process can be expressed in terms of elementary functions. It is also found that in the absence of absorption the high-frequency dielectric constant of a composite material with different signs of the initial dielectric constants ε does not converge to a limit and is an oscillatory function of the frequency and n. Finally, for massive and thin-film samples, the local plasmon frequencies in the medium are established. Zh. éksp. Teor. Fiz. 114, 669–675 (August 1998)     

Electron mobility in a disordered medium of dipole scatterers

A theory has been developed which suggests a possible explanation of a considerable discrepancy, recently experimentally discovered in dense water and ammonia vapours, between the electronic mobility values measured and calculated from the Lorentz formula.     

Random lasing in strongly disordered medium

Using the time-dependent theory, we calculate the random-laser emission spectra in a two-dimensional strongly disordered medium. The calculation results show that in low dimensional systems, such as thin- film disordered media and planar waveguides, the larger the difference of the refractive indices between the scattering and background media, the smaller the lasing threshold. We also reveal the existence of multi-mode survival and mode competition. We experimentally obtain the emission spectra of a dye solution with Al particles doped at different pumping energies, and the experimental results agree well with the calculated ones.     

Relaxation length of a polymer chain in a quenched disordered medium

Using Monte Carlo simulations, we study the relaxation and short-time diffusion of polymer chains in two-dimensional periodic arrays of obstacles with random point defects. The displacement of the center of mass follows the anomalous scaling law r(c.m.)(t)(2)=4D(*)t(beta), with beta<1, for times t相似文献   

Time-resolved phase-space distributions for light backscattered from a disordered medium

We demonstrate time-resolved measurement of optical phase-space distributions as a new probe for investigating the propagation of light in disordered media. Phase-space techniques measure the joint transverse position and momentum distribution of the scattered light, and are sensitive to the spatially varying phase and amplitude of the field. Using this method we investigate light backscattered from a random medium. The measurements indicate that the weakly localized component is a phase conjugate of the incident light field. A new model of backscatter, based on Wigner phase-space distributions, elucidates the spatial and angular behavior of the localized and unlocalized components.     

Superfluid properties of magnetized 3He-B in a disordered medium

The influence of nonmagnetic impurity scattering on the anisotropy of the magnetized B phase of superfluid ³He is investigated theoretically. The contribution of the impurity-induced spin-singlet superfluid correlations in the presence of the p-wave Cooper pairing is revealed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 95–100 (25 January 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Diffusion in a disordered porous medium with localized phase transitions on the pore walls

We derive expressions for the mean ionic components densities of a solution diffusing in a disordered, porous medium. These expressions take into account interphase processes at the pore walls, such as crystallization of salts of the diffusing ionic component. Russian Friends of the Peoples University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 24–31, January, 1997.     

Coherent backscattering of a light pulse by a slab of disordered medium

We obtain an exact analytical solution to the problem of the enhanced backscattering of a short pulsed signal from a two- and three-dimensional medium with isotropically scattering centres. The angular spectrum is expressed in terms of the solution to the corresponding stationary problem. The intensity oscillations are shown to appear on the tails of the angular spectrum. The origin of these oscillations is associated with the ballistic phase shift between the interfering waves arriving at the detector. It is shown that the finiteness of the slab thickness influences the magnitude of the backscattering intensity and does not change the shape of the angular spectrum. The range of validity for the diffusion approximation is pointed out.

The results obtained in the paper also contain a generalization of the well known solution to the problem of incoherent transfer to a pulsed signal to the case of two-dimensional disordered media.     

Transport in a disordered medium: Analysis and Monte Carlo simulation

We consider a classical stochastic model describing particle transport on a lattice with randomly distributed nearest-neighbor transition rates. Applying an effective medium theory to the model, we determine average properties related to the particle's dynamics ind-dimensions. In particular, we calculate the mean-square displacement, and the fourth moment of the displacement in one-, two- and three dimensions. The results compare favorably with Monte Carlo simulations of the model. We also present preliminary results for the velocity autocorrelation function.An aspect of the bond percolation problem, which is a special case of the stochastic model is investigated; the average inverse cluster size, <N _c ^–1>, is calculated. In one dimension the expression for this quantity is exact and in higher dimensions our results are very accurate not too close to the percolation concentration.     

On the stability of time-harmonic localized states in a disordered nonlinear medium

We study the problem of localization in a disordered one-dimensional nonlinear medium modeled by the nonlinear Schrödinger equation. Devillard and Souillard have shown that almost every time-harmonic solution of this random PDE exhibits localization. We consider the temporal stability of such time-harmonic solutions and derive bounds on the location of any unstable eigenvalues. By direct numerical determination of the eigenvalues we show that these time-harmonic solutions are typically unstable, and find the distribution of eigenvalues in the complex plane. The distributions are distinctly different for focusing and defocusing nonlinearities. We argue further that these instabilities are connected with resonances in a Schrödinger problem, and interpret the earlier numerical simulations of Caputo, Newell, and Shelley, and of Shelley in terms of these instabilities. Finally, in the defocusing case we are able to construct a family of asymptotic solutions which includes the stable limiting time-harmonic state observed in the simulations of Shelley.     

Elastoelectric effect in a disordered homogeneous nonconducting medium under centrosymmetric external influences

Within a variational approach, a system of nonlinear equations is obtained to analyze elastoelectric effects in a disordered homogeneous nonconducting medium. The results of analysis are applied to the case of a spherical shell subject to centrosymmetric hydrostatic pressure from outside and inside.