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Motivated by the link between Anderson localisation on high-dimensional graphs and many-body localisation, we study the effect of periodic driving on Anderson localisation on random trees. The time dependence is eliminated in favour of an…
We present a numerical study of electromagnetic wave transport in disordered quasi-one-dimensional waveguides at terahertz frequencies. Finite element method calculations of terahertz wave propagation within LiNbO$_{3}$ waveguides with…
We present a new embedding scheme for the locally self-consistent method to study disordered electron systems. We test this method in a tight-binding basis and apply it to the single band Anderson model. The local interaction zone is used…
We show that the recently developed self-consistent theory of Anderson localization with a position-dependent diffusion coefficient is in quantitative agreement with the supersymmetry approach up to terms of the order of $1/g_0^2$ (with…
Anderson localisation is an important phenomenon arising in many areas of physics, and here we explore it in the context of quantum information devices. Finite dimensional spin chains have been demonstrated to be important devices for…
Signatures of strong Anderson localization in the momentum distribution of a cold atom cloud after a quantum quench are studied. We consider a quasi one-dimensional cloud initially prepared in a well defined momentum state, and expanding…
We calculate the effective spatial dimension $d_\text{IR}$ of electron modes at critical points of 3D Anderson models in various universality classes (O,U,S,AIII). The results are equal within errors, and suggest the super-universal value…
We study Anderson localization in a discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength $\theta$ and quasienergies located on the unit circle. We demonstrate that strong disorder in a local phase field…
We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the…
Dynamical localization phenomena of monochromatically perturbed standard map (SM) and Anderson map (AM), which are both identified with a two-dimensional disordered system under suitable conditions, are investigated by the numerical…
We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the…
Localization and delocalization of quantum diffusion in time-continuous one-dimensional Anderson model perturbed by the quasi-periodic harmonic oscillations of $M$ colors is investigated systematically, which has been partly reported by the…
Searching for Anderson localization of light in three dimensions has challenged experimental and theoretical research for the last decades. Here the problem is analyzed through large scale numerical simulations, using a radiative…
Anderson localization does not lead to an exponential decay of intensity of an incident wave with the depth inside a strongly disordered three-dimensional medium. Instead, the average intensity is roughly constant in the first half of a…
A new approach is applied to the 1D Anderson model by making use of a two-dimensional Hamiltonian map. For a weak disorder this approach allows for a simple derivation of correct expressions for the localization length both at the center…
The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are…
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…
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…
In this paper, the influence of the quasidisorder on a two-dimensional system is studied. We find that there exists a topological phase transition accompanied by a transverse Anderson localization. The topological properties are…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…