Coherent Multiple Backscattering of Waves in Random Medium beyond the Diffusion Approximation

Peter Slavov

Home/Archive/arXiv

arXiv · cond-mat/0610026

Coherent Multiple Backscattering of Waves in Random Medium beyond the Diffusion Approximation

Peter Slavov

View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper the validity of the diffusion approximation for multiple scattering of classical waves in random medium in different regimes is investigated, with emphasize to weak localization effects. Many principle topics are discussed once again. We obtain new expressions for the incoherent and coherent multiple scattering intensities for the more general case of large scattering angles and various observation points inside the medium with moving scatterers and absorption. (The results, we reached, assuming white-noise disorder for the impurities correlator, contain one-dimensional integration in its final analytical form). Also new self-consistent formulas for incoherent and coherent intensities for fixed multiplicity orders of scattering are given and their lineshapes are graphically represented. Through these formulas we clearly demonstrate that the impurities motion reduces the contribution to the intensity of the scatterings with large multiplicity orders. The total scattering intensities in $4π$ solid angle are calculated for the general case and compared with their diffusion approximation. For coherent intensities it is shown that a drastic deviation from the exact results occurs. It turns out that the region of angles, for which the observed lineshape of the weak localization effect tends to the incoherent background, give the main contribution to the total coherent scattered intensity. The last quantity happens to depend linearly instead of predicted quadratic dependence on the perturbation parameter, 1/kl.

Explore related subjects

cond-mat.dis-nn cond-mat.mes-hall

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Peter Slavov. 2006-10-01. Coherent Multiple Backscattering of Waves in Random Medium beyond the Diffusion Approximation. https://arxiv.org/abs/cond-mat/0610026

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Irrationality Measure Controls Long-Wavelength Charge Fluctuations in Quasiperiodic Systems

Quasiperiodic order is characterized by irrational frequencies whose rational approximability known as irrationality measure defines distinct arithmetic classes. We establish that this arithmetic classification has direct physical consequences for long-wavelength charge fluctuations. In translation-covariant quasiperiodic systems, the infrared scaling of charge fluctuation is governed by the interplay between the irrationality exponent of irrational frequency and the large-harmonic decay of the hull charge profile: the latter determines the available charge weight, while the former controls how efficiently that weight is transferred to the infrared. Consequently, all algebraic irrational frequencies share the same arithmetic scaling, whereas exceptionally well-approximable transcendental frequencies can exhibit strongly enhanced infrared fluctuation scaling. We further prove that occupied states separated from the Fermi level by a gap stable throughout the hull contribute only an analytic infrared background, leaving the nontrivial scaling to near-Fermi states. Our results extend to general translation-covariant multi-frequency quasiperiodic systems.

cond-mat.dis-nn↗

arXiv2026

Curvature-Induced Geometric Universality in Non-Hermitian Anderson Transitions

In Euclidean space, universality classes of Anderson transitions are primarily determined by symmetry and spatial dimensionality. Here, we present evidence for a geometry-controlled universality class of non-Hermitian Anderson transitions on hyperbolic-like lattices. In this setting, critical behavior is influenced by the large-scale hyperbolic geometry, characterized by negative curvature, exponential volume growth, and a non-Euclidean notion of spatial scaling. Finite-size scaling of participation ratios across several distinct $ \{p,q\} $ tilings reveals one-parameter scaling collapses with a common critical exponent $ \nu\simeq1 $ within numerical accuracy. A complementary phenomenological coarse-grained Landau-Ginzburg analysis shows how exponential correlation-volume growth suppresses critical fluctuations, offering a rationale for the observed mean-field-like scaling. Our results suggest that spatial curvature can act as an additional organizing principle for Anderson-transition universality beyond the conventional dimensionality- and symmetry-based classification.

cond-mat.dis-nn↗

arXiv2026

Finite-rank multiplicative perturbations of rotationally invariant non-Hermitian random matrices

We study finite-rank multiplicative deformations of rotationally invariant non-Hermitian random matrices. More precisely, we consider models of the form $\mathbf{A}(\mathbf{I}+\mathbf{T})$, where $\mathbf{A}$ is a large rotationally invariant non-Hermitian random matrix, $\mathbf{T}$ is a finite-rank normal perturbation, and $\mathbf{I}$ denotes the identity matrix. We characterize the emergence of outlier eigenvalues, their fluctuations, and the associated eigenvector overlaps. Our results provide a multiplicative non-Hermitian counterpart to the classical Baik--Ben Arous--P\'ech\'e framework.

cond-mat.dis-nn↗