Related papers: One Parameter Scaling Theory for Stationary States…
In machine learning, the scaling law describes how the model performance improves with the model and data size scaling up. From a learning theory perspective, this class of results establishes upper and lower generalization bounds for a…
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…
The spectral approach to infinite disordered crystals is applied to an Anderson-type Hamiltonian to demonstrate the existence of extended states for nonzero disorder in 2D lattices of different geometries. The numerical simulations shown…
We study the influence of boundary conditions transverse to the transport direction for disordered mesoscopic conductors both at the Anderson metal-insulator transition and in the metallic regime. We show that the boundary conditions…
We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the…
We investigate numerically the statistical properties of spectra of two-dimensional disordered systems by using the exact diagonalization and decimation method applied to the Anderson model. Statistics of spacings calculated for system…
We numerically study the Anderson localization of weekly interacting Bose-Einstein condensate in a one-dimensional disordered potential. We show that two parameters are needed to completely describe such system, and the density profile of…
The scaling properties of the wave functions in finite samples of the one dimensional Anderson model are analyzed. The states have been characterized using a new form of the information or entropic length, and compared with analytical…
We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain \emph{typical local density of states} as an order parameter, thereby reproducing the essential features of a phase-diagram of…
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…
We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric…
Scale-free localization emerging in non-Hermitian physics has recently garnered significant attention. In this work, we explore the interplay between scale-free localization and Anderson localization by investigating a unidirectional…
Motivated by mapping from a stochastic system with spatially random rates, we consider disordered non-conserving free-fermion systems using a scaling procedure for the equations of motion. This approach demonstrates disorder-induced…
It is shown that the Anderson transition (AT) in 3d obeys a two-parameter scaling law, derived from a pair of anisotropic scaling transformations, and corresponding critical exponents and scaling function calculated, using a high-precision…
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…
Localization is one of the most fundamental interference phenomena caused by randomness, and its universal aspects have been extensively explored from the perspective of one-parameter scaling mainly for static properties. We numerically…
If disorder-induced Anderson localized states have been observed experimentally in optics, their study remains challenging leaving a number of open questions unsolved. Among them, the impact on Anderson localization of non-Hermiticity,…
We study the affinities between the shape of the bright soliton of the one-dimensional nonlinear Schroedinger equation and that of the disorder induced localization in the presence of a Gaussian random potential. With emphasis on the…
The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is…
We show that, in contrast to immediate intuition, Anderson localization of noninteracting particles induced by a disordered potential in free space can increase (i.e., the localization length can decrease) when the particle energy…