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The most recent manifestation of cold Rydberg atom quantum simulators that employs tailored optical tweezer arrays enables the study of many-body dynamics under so-called facilitation conditions. We show how the facilitation mechanism…
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…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
We present a novel model to calculate single-electron states in random quantum dot superlattices made of wide-gap semiconductors. The source of disorder comes from the random arrangement of the quantum dots (configurational disorder) as…
We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…
We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns…
Domain adaptation aims to bridge the domain shifts between the source and the target domain. These shifts may span different dimensions such as fog, rainfall, etc. However, recent methods typically do not consider explicit prior knowledge…
Latent Dirichlet allocation (LDA) obtains essential information from data by using Bayesian inference. It is applied to knowledge discovery via dimension reducing and clustering in many fields. However, its generalization error had not been…
We discuss vibrational localization problems in glasses and disordered media in this paper. It is claimed that the essence of the localization problem is already observed in disordered lattice models. These kinds of vibrations belong to a…
We develop a formalism to study the role of local defects in tight binding systems in the presence of a strong external ac electric field. It is found that the appearance and disappearance of localized states, as well as their localization…
We study the critical behaviour of Anderson localized modes near intersecting flat and dispersive bands in the quasi-one-dimensional diamond ladder with weak diagonal disorder $W$. The localization length $\xi$ of the flat band states…
This work addresses the Galerkin isogeometric discretization of the one-dimensional Laplace eigenvalue problem subject to homogeneous Dirichlet boundary conditions on a bounded interval. We employ GLT theory to analyze the behavior of the…
In this paper we analyze the existence, stability, dynamical formation and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schr\"{o}dinger equation with a linear point defect. We…
We develop the generalized rotating-wave approximation (GRWA) approach (Phys. Rev. Lett. 99, 173601 (2007)) to study the single-photon scattering on a two-level system (TLS) with arbitrarily strong coupling to a local mode in a…
For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…
Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. The underlying mechanism for this localization behaviour has however remained elusive. We provide here an analysis of locally…
We study the defect (or "signed area") distribution of toral Laplace eigenfunctions restricted to shrinking balls of radius above the Planck scale, in either random Gaussian scenario ("Arithmetic Random Waves"), or deterministic…
We compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter- and intra-module degree distributions, subject only to the constraint of finite mean connectivities. We also evaluate…
We have been investigating the problem of the Anderson localization in a disordered one dimensional tight-binding model. The disorder is created by the interaction of mobile particles with other species, immobilized at random positions. We…
We compare the spectrum and the localisation properties of the eigenmodes of the Laplacian and the adjacency matrix of 2D random geometric graphs, using numerical diagonalization of these matrices for different system sizes and…