Related papers: Analysis of localization-delocalization transition…
The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at…
The unidirectional Hatano-Nelson chain serves as the fundamental non-Hermitian building block of the Su-Schrieffer-Heeger (SSH) model. We investigate its Anderson localization properties under diagonal binary disorder. For weak disorder,…
We investigate the transition from the many-body localized phase to the ergodic thermalized phase at an infinite temperature in an $XY$ spin chain with $L$ spins, which experiences power-law decaying interactions in the form of…
We study the interplay of disorder and interaction effects including bosonic degrees of freedom in the framework of a generic one-dimensional transport model, the Anderson-Edwards model. Using the density-matrix renormalization group…
Using a three-frequency one-dimensional kicked rotor experimentally realized with a cold atomic gas, we study the transport properties at the critical point of the metal-insulator Anderson transition. We accurately measure the…
We study numerically the effects of nonlinearity on the Anderson localization in lattices with disorder in one and two dimensions. The obtained results show that at moderate strength of nonlinearity an unlimited spreading over the lattice…
We implement an efficient strong-disorder renormalization-group (SDRG) procedure to study disordered tight-binding models in any dimension and on the Erdos-Renyi random graphs, which represent an appropriate infinite dimensional limit. Our…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation…
We study quench dynamics in an interacting spin chain with a quasi-periodic on-site field, known as the interacting Aubry-Andr\'e model of many-body localization. Using the time-dependent variational principle, we assess the late-time…
We study a random Schroedinger operator, the Laplacian with random Dirac delta potentials on a torus T^d_L = R^d/LZ^d, in the thermodynamic limit L\to\infty, for dimension d=2. The potentials are located on a randomly distorted lattice…
In a recent experiment [X. Yu et al., arXiv:2602.07654], energy-resolved measurements of an atomic matter wave spreading in a speckle potential enabled the direct observation of the three-dimensional Anderson transition. In this work, we…
These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…
In the most popular approach to the numerical study of the Anderson metal-insulator transition the transfer matrix method is combined with finite-size scaling ideas. This approach requires large computer resources to overcome the…
According to the Anderson theorem, the critical temperature T_c of a disordered superconductor is determined by the average density of states and does not change at the localization threshold. This statement is valid under assumption of a…
Light localization by scattering is a fundamental mechanism driving phase transitions of wave transport in disordered systems. Characterizing the localization length in scattering systems is crucial yet challenging. In this Letter, we…
The energy level spacing distribution of a tight-binding hamiltonian is monitored across the mobility edge for a fixed disorder strength. Any mixing of extended and localized levels is avoided in the configurational averages, thus…
We revisit the Anderson localization problem on Bethe lattices, putting in contact various aspects which have been previously only discussed separately. For the case of connectivity 3 we compute by the cavity method the density of states…
We present an eigensystem multiscale analysis for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model in an energy interval. In particular, it yields…
We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at…
Anderson localization, i.e. the suppression of diffusion in lattices with random or incommensurate disorder, is a fragile interference phenomenon which is spoiled out in the presence of dephasing effects or fluctuating disorder. As a…