Related papers: Anderson transition in high dimension: comments to…
We study Anderson transition for light in three dimensions by performing large-scale ab-initio simulations of electromagnetic wave transport in disordered ensembles of conducting spheres. A mobility edge that separates diffusive transport…
Anderson localization is fundamentally controlled by dimensionality, yet the nature of the Anderson transition in continuously tunable noninteger dimensions remains largely unexplored. Here, we introduce a family of three-dimensional…
The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are…
This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are…
We study the Anderson transition for three-dimensional (3D) $N \times N \times N$ tightly bound cubic lattices where both real and imaginary parts of onsite energies are independent random variables distributed uniformly between $-W/2$ and…
Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways (cf. [Lub94], [HLW06], [Lub12] and the…
We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the…
We study the dependence on the spatial dimensionality of different quantities relevant in the description of the Anderson transition by combining numerical calculations in a $3 \leq d \leq 6$ disordered tight binding model with theoretical…
Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…
We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional…
Hyperbolic lattices, formed by tessellating the hyperbolic plane with regular polygons, exhibit a diverse range of exotic physical phenomena beyond conventional Euclidean lattices. Here, we investigate the impact of disorder on hyperbolic…
We introduce a new combinatorial abstraction for the graphs of polyhedra. The new abstraction is a flexible framework defined by combinatorial properties, with each collection of properties taken providing a variant for studying the…
We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe…
In disordered systems, our present understanding of the Anderson transition is hampered by the possible presence of interactions between particles. We demonstrate that in boson gases, even weak interactions deeply alter the very nature of…
We use two different fully vectorial microscopic models featuring nonresonant and resonant scattering, respectively, to demonstrate the Anderson localization transition for elastic waves in three-dimensional (3D) disordered solids. Critical…
An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that…
We study the gradual transition from one-dimensional to two-dimensional Anderson localization upon transformation of the dimensionality of disordered waveguide arrays. An effective transition from one- to two-dimensional system is achieved…
Existence of the upper critical dimension d_{c2}=4 for the Anderson transition is a rigorous consequence of the Bogoliubov theorem on renormalizability of \phi^4 theory. For dimensions d\ge 4, one-parameter scaling does not hold, and all…
Nonreciprocity breaks the symmetry between forward and backward propagation, giving rise to a range of peculiar wave phenomena. In this work, we investigate Anderson localization in higher-dimensional nonreciprocal lattices. Focusing on the…
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…