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Localization-delocalization transition in a discrete Anderson nonlinear Schr\"odinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity…
We have identified a new type of transition from extended to localized vibrational states in one-dimensional graded elastic chains of coupled harmonic oscillators, in which the vibrating masses or nearest-coupling force constants vary…
We investigate the localization behavior of electrons in a random lattice which is constructed from a quasi-one-dimensional chain with large coordinate number $Z$ and rewired bonds, resembling the small-world network proposed recently but…
We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are…
The localization lengths of long-range correlated disordered chains are studied for electronic wavefunctions in the Anderson model and for vibrational states. A scaling theory close to the band edge is developed in the Anderson model and…
Quantum site percolation as a limiting case of binary alloy is studied numerically in 2D within the tight-binding model. We address the transport properties in all regimes - ballistic, diffusive (metallic), localized and crossover between…
We study the effect of spatially correlated classical noise on both Anderson and many-body localization of a disordered fermionic chain. By analyzing the evolution of the particle density imbalance following a quench from an initial charge…
The use of quantum entanglement to study condensed matter systems has been flourishing in critical systems and topological phases. Additionally, using real-space entanglement entropies and entanglement spectra one can characterize localized…
The three-dimensional Anderson model with a rectangular distribution of site disorder displays two distinct localization-delocalization transitions, against varying disorder intensity, for a relatively narrow range of Fermi energies. Such…
Anderson transition of the phonon modes is studied numerically. The critical exponent for the divergence of the localization length is estimated using the transfer matrix method, and the statistics of the modes is analyzed. The latter is…
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…
We investigate light transport in three-dimensional disordered media composed of irregular dielectric particles using large scale full-wave simulations. For subwavelength particles with size parameter $kr \approx 1$ and high refractive…
Besides the dynamical slowing down signaled by an enormous increase of the viscosity approaching the glass transition, structural glasses show interesting anomalous thermodynamic features at low temperatures that hint at peculiar deviations…
Using a quantum map version of one-dimensional Anderson model, the localization-delocalization transition of quantum diffusion induced by coherent dynamical perturbation is investigated in comparison with quantum standard map. Existence of…
The Anderson localization of thermal phonons has been shown only in few nano-structures with strong random disorder by the exponential decay of transmission to zero and a thermal conductivity maximum when increasing system length. In this…
Using the level--spacing distribution and the total probability function of the numbers of levels in a given energy interval we analyze the crossover of the level statistics between the delocalized and the localized regimes. By numerically…
Based on the statistical dynamical mean field theory, we investigate, in a generic model for a strongly coupled disordered electron-phonon system, the competition between polaron formation and Anderson localization. The statistical…
Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold…
We consider the localization properties of a lattice of coupled masses and springs with random mass and spring constant values. We establish the full phase diagrams of the system for pure mass and pure spring disorder. The phase diagrams…
The translational symmetry of solids gives rise to the existence of low-frequency phonons. In ordered systems, some phonons characterized by different wavevectors are degenerate, i.e. they share the same frequency $\omega$; in finite-size…