Related papers: Anderson transition for elastic waves in three dim…

The wavefunctions of a disordered two-dimensional electron gas at the quantum-critical Anderson transition are predicted to exhibit multifractal scaling in their real space amplitude. We experimentally investigate the appearance of these…

Critically analyzing recent STM and transport experiments [Z. Ge, et al, arXiv:2510.12009] on 2D electron systems in the presence of random quenched impurities, we argue that the resulting low-density putative "solid" phase reported…

In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…

A theory for multiple scattering of elastic waves is presented in a random medium bounded by two ideal free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. This geometry…

The three-dimensional Anderson model represents a paradigmatic model to understand the Anderson localization transition. In this work we first review some key results obtained for this model in the past 50 years, and then study its…

We clarify universal critical properties of delocalization-localization transitions in three-dimensional (3D) unitary and orthogonal classes with particle-hole and/or chiral symmetries (classes AIII, BDI, D, C and CI). We first introduce…

We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson - nonlinear…

We study three-dimensional optical Anderson localization in medium with a percolating disorder, where the percolating clusters are filled by the light nanoemitters in the excited state. The peculiarity of situation is that in such materials…

We study the critical behaviour of Anderson localized modes near intersecting flat and dispersive bands in the quasi-one-dimensional diamond ladder with weak diagonal disorder $W$. The localization length $\xi$ of the flat band states…

A solid transparent medium with randomly positioned, immobile impurity atoms is a promising candidate for observation of Anderson localization of light in three dimensions. It can have low losses and allows for mitigation of the detrimental…

This tutorial review gives an overview of the transverse Anderson localization of light in one and two transverse dimensions. A pedagogical approach is followed throughout the presentation, where many aspects of localization are illustrated…

We investigate Anderson transitions for a system of two particles moving in a three-dimensional disordered lattice and subject to on-site (Hubbard) interactions of strength U. The two-body problem is exactly mapped into an effective…

Elastic waves scattering off a periodic single and double array of thin cylindrical defects is considered for isotropic materials. An analytical expression for the scattering matrix is obtained by means of the Lippmann-Schwinger formalism…

We establish a phase diagram of a model in which scalar waves are scattered by resonant point scatterers pinned at random positions in the free three-dimensional (3D) space. A transition to Anderson localization takes place in a narrow…

As discovered by Philip Anderson in 1958, strong disorder can block propagation of waves and lead to the localization of wave-like excitations in space. Anderson localization of light is particularly exciting in view of its possible…

In this article, we study the Anderson Hamiltonian in the full space and prove wellposedness of nonlinear stochastic wave equation and NLS with polynomial nonlinearities.

In dissipationless linear media, spatial disorder induces Anderson localization of matter, light, and sound waves. The addition of nonlinearity causes interaction between the eigenmodes, which results in a slow wave diffusion. We go beyond…

We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of…

Scattering theoretical network models for general coherent wave mechanical systems with quenched disorder are investigated. We focus on universality classes for two dimensional systems with no preferred orientation: Systems of spinless…

We report a finite size scaling study of the Anderson transition. Different scaling functions and different values for the critical exponent have been found, consistent with the existence of the orthogonal and unitary universality classes…