Nonlinear coherent transport of waves in disordered media

We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. We show that the coherent backscattering enhancement factor is strongly affected by the nonlinearity, and we corroborate these results by numerical simulations. Our theory can be applied to several physical scenarios such as scattering of light in a nonlinear Kerr medium or propagation of matter waves in disordered potentials.     

Nature of coherent enhancement of inelastic electron scattering from disordered media

The mechanism of weak localization of relatively fast electrons scattered with a fixed energy loss from disordered media is examined. The main focus of this paper is to put forward an explanation for why coherent enhancement of electron scattering in the inelastic-scattering channel takes place at angles which differ from π. A simplified kinematic model is proposed to determine the basic properties of the weak localization of electrons in the inelastic scattering channel. The model easily reproduces the range of scattering angles typical for the weak localization of electrons with fixed energy loss. The procedure does not require calculation of the contribution from the crossed diagrams. The results agree with those based on the dynamical theory associated with the calculation of the crossed and ladder diagrams. It is possible to follow the transition from the weak localization of the new type to the ordinary weak localization with decreasing energy loss. The weak localization of the new type is in accord with the weak localization of regular type if the energy loss is about the energy of an optical phonon.     

New quasiparticles hystons and coherent photoinduced dynamics of molecules in polar disordered media

Using methods of statistical thermodynamics, it is shown that after pulse excitation the evolution of a “polar luminescent probe—polar disordered medium” system is described by an equation of damping vibrations. This allows the conclusion that in the solvate shell of the probe molecule synchronous rotational vibrations (librations) of the molecules of the medium occur, whose damping is caused by dielectric friction. Such a collective synchronous motion is considered as a motion of a quasiparticle called a hyston. The moment of inertia J_n and mass M_h of a hyston are defined as J_h=2m² ₁a^-3Ω₀ ^-2(ε-1)/(2ε+1), M_h=J_hM_s/J_s, where m₁ is the dipole moment of the probe molecule in the excited S₁-stute; a is the Onsager radius; Ω₀ is the cyclic frequency of harmonic vibrations of the hyston; ε is the dielectric constant; M_s and J_s are the mass and moment of inertia of a molecule of the medium, respectively. The correlation function of the motion of the molecules c(t) is a solution of the equation of hyston motion. The fluorescence response s(t) in measurements with time resolution coincides with the correlation function: s(t)=c(t). The concepts concerning hystons make it possible to describe macroscopic photoinduced coherent motion that is manifested against a background of thermal motion of the medium molecules. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnei Spektroskopii, Vol 65, No. 2, pp. 176–183, March–April, 1998.     

Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the 'ant in the labyrinth') on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the ‘ant in the labyrinth’) on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

New effects in light scattering in disordered media and coherent backscattering cone: systems of magnetic particles

Single and multiple scattering of light by magnetic particles and their implications to the coherent backscattering effect are reported. Single scattering of light by small magnetic particles presents unusual features such as forward-backward asymmetry and resonance effects. In multiple scattering, this leads to a global decrease in the localization parameter kl(*), which exhibits an oscillatory dependence on the scatterer magnetic permeability. By considering magnetic scatterers following a Curie-Weiss susceptibility law, we suggest that kl(*) can be tuned by varying the temperature.     

Superconductor-insulator transition in disordered boson-superlattices

We calculate the transport properties of a disordered Bose condensate. A superlattice made from two-dimensional planes of bosons in the condensate phase is considered. The disorder is due to charged impurities. We consider a homogeneous distribution of impurities and also impurities randomly distributed in planes. The dispersion relation of the collective excitations (plasmons) for the clean boson superlattice is calculated. The disorder induced phase transiton from a superfluid phase to an insulator phase is discussed and the static conductivity ( _c ) at the transition point is expressed in terms of the microscopic parameters of the model. For strongly coupled planes we find that _c is of ordere ²/h. The relation of our theoretical results to experiments with high-temperature superconductors is discussed.     

Spin-glass transition in disordered terbium

While crystalline Tb is a helix antiferromagnet with a Néel temperature of 229 K which becomes ferromagnetic at 222 K, disordered Tb exhibits a spin-glass transition. The spin-glass freezing temperature ranges from 183 to 53 K, the lowest temperatures corresponding to the greatest degree of atomic disorder. These experiments constitute the first evidence for an elemental spin-glass.     

Dielectric resonances in disordered media

Binary disordered systems are usually obtained by mixing two ingredients in variable proportions: conductor and insulator, or conductor and super-conductor. They present very specific properties, in particular the second-order percolation phase transition, with its fractal geometry and the multi-fractal properties of the current moments. These systems are naturally modeled by regular bi-dimensional or tri-dimensional lattices, on which sites or bonds are chosen randomly with given probabilities. The two significant parameters are the ratio h = σ ₁/σ of the complex conductances, σ and σ ₁, of the two components, and their relative abundances p (or, respectively, 1 - p). In this article, we calculate the impedance of the composite by two independent methods: the so-called spectral method, which diagonalises Kirchhoff's Laws via a Green function formalism, and the Exact Numerical Renormalization method (ENR). These methods are applied to mixtures of resistors and capacitors (R-C systems), simulating e.g. ionic conductor-insulator systems, and to composites constituted of resistive inductances and capacitors (LR-C systems), representing metal inclusions in a dielectric bulk. The frequency dependent impedances of the latter composites present very intricate structures in the vicinity of the percolation threshold. In this paper, we analyse the LR-C behavior of compounds formed by the inclusion of small conducting clusters (“n-legged animals”) in a dielectric medium. We investigate in particular their absorption spectra who present a pattern of sharp lines at very specific frequencies of the incident electromagnetic field, the goal being to identify the signature of each animal. This enables us to make suggestions of how to build compounds with specific absorption or transmission properties in a given frequency domain. Received 16 August 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: laurent.raymond@l2mp.fr RID="b" ID="b"e-mail: steffen.schaefer@l2mp.fr RID="c" ID="c"UMR CNRS 6137     

"Bending to stretching" transition in disordered networks

From polymer gels to cytoskeletal structures, random networks of elastic material are commonly found in both materials science and biology. We present a three-dimensional micromechanical model of these networks and identify a "bending-to-stretching" transition. We characterize this transition in terms of concentration scaling laws, the stored elastic energy, and affinity measurements. Understanding the relationship between microscopic geometry and macroscopic mechanics will elucidate, for example, the mechanical properties of polymer gel networks or the role of semiflexible network mechanics in cells.     

Radiation trapping in coherent media

We show that the effective decay rate of Zeeman coherence, generated in a (87)Rb vapor by linearly polarized laser light, increases significantly with the atomic density. We explain this phenomenon as the result of radiation trapping. Our study shows that radiation trapping must be taken into account to fully understand many electromagnetically induced transparency experiments with optically thick media.