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We present an extended microcanonical Lanczos method (MCLM) for a direct evaluation of the diffusion constant and its frequency dependence within the disordered Anderson model of noninteracting particles. The method allows to study systems…
The Anderson delocalization-localization transition is studied in multilayered systems with randomly placed interlayer bonds of density $p$ and strength $t$. In the absence of diagonal disorder (W=0), following an appropriate perturbation…
We study the effect of disorder in a holographic superconductor by introducing a quasi-periodic chemical potential. When the condensation of the superconductor is sufficiently small compared with the strength of disorder, we find that there…
In this paper we review results of Anderson localization for different random families of operators which enter in the framework of random quasi-one-dimensional models. We first recall what is Anderson localization from both physical and…
In this paper, we developed a new parametrization method to calculate the localization length in one-dimensional Anderson model with diagonal disorder. This method can avoid the divergence difficulty encountered in the conventional methods,…
We develop a mathematical framework that interprets Transformer attention as an interacting particle system and studies its continuum (mean-field) limits. By idealizing attention on the sphere, we connect Transformer dynamics to Wasserstein…
Instance-level alignment is widely exploited for person re-identification, e.g. spatial alignment, latent semantic alignment and triplet alignment. This paper probes another feature alignment modality, namely cluster-level feature alignment…
We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on $\ZZ^d$. We establish geometric…
It is typically assumed that disorder is essential to realize Anderson localization. Recently, a number of proposals have suggested that an interacting, translation invariant system can also exhibit localization. We examine these claims in…
We find that Anderson localization ceases to exist when a random medium begins to move, but another type of fundamental quantum effect, Planckian diffusion $D = \alpha\hbar/m$, rises to replace it, with $\alpha $ of order of unity.…
At low temperature, a quasi-one-dimensional ensemble of atoms with attractive interaction forms a bright soliton. When exposed to a weak and smooth external potential, the shape of the soliton is hardly modified, but its center-of-mass…
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…
Anderson localization is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium. Unlike in a classical resonator, satisfying the favorable condition for the interference in a disordered medium is truly…
Solutions of the wave equations for time-independent disordered media can exhibit Anderson localization where instead of wave propagation we observe their localization around different points in space. Photonic time crystals are spatially…
Anderson localization confines the wave function of a quantum particle in a one-dimensional random potential to a volume of the order of the localization length $\xi$. Nonlinear add-ons to the wave dynamics mimic many-body interactions on a…
We study temperature induced metal-insulator transition in doped ferromagnetic semiconductors, described by s-d exchange model. The transition is a result of the mobility edge movement, the disorder being due to magnetic ions spin density…
Influence of disorder on the temperature of superconducting transition (T_c) is studied within the sigma-model renormalization group framework. Electron-electron interaction in particle-hole and Cooper channels is taken into account and…
In this paper, we use recent breakthroughs in the study of coupled subwavelength resonator systems to reveal new insight into the mechanisms responsible for the fundamental features of Anderson localization. The occurrence strong…
We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…
The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered…