Related papers: Spectral properties of three-dimensional Anderson …
We study the transport of classical waves through three-dimensional (3D) anisotropic media close to the Anderson localization transition. Time-, frequency-, and position-resolved ultrasonic measurements are performed on anisotropic…
Localization-delocalization transition in a discrete Anderson nonlinear Schr\"odinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity…
A review of recent progress in numerical studies of the Anderson transition in three dimensional systems is presented. From high precision calculations the critical exponent $\nu$ for the divergence of the localization length is estimated…
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…
We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization…
For disordered interacting quantum systems, the sensitivity of the spectrum to twisted boundary conditions depending on an infinitesimal angle $\phi$ can be used to analyze the Many-Body-Localization Transition. The sensitivity of the…
We examine statistical fluctuation of eigenvalues from the near-edge bulk of QCD Dirac spectra above the critical temperature. For completeness we start by reviewing on the spectral property of Anderson tight-binding Hamiltonians as…
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…
Anderson localization transitions are a universal quantum phenomenon sensitive to the disorder and dimensionality of electronic systems. Over the past decades, this intriguing topic has inspired overwhelmingly more theoretical studies than…
We study Anderson localisation on high-dimensional graphs with spatial structure induced by long-ranged but distance-dependent hopping. To this end, we introduce a class of models that interpolate between the short-range Anderson model on a…
We study the level-spacing distribution function $P(s)$ at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution…
After exactly half a century of Anderson localization, the subject is more alive than ever. Direct observation of Anderson localization of electrons was always hampered by interactions and finite temperatures. Yet, many theoretical…
A field theory of the Anderson transition in two dimensional disordered systems with spin-orbit interactions and time-reversal symmetry is developed, in which the proliferation of vortex-like topological defects is essential for…
We study the Anderson-type transition previously found in the spectrum of the QCD quark Dirac operator in the high temperature, quark-gluon plasma phase. Using finite size scaling for the unfolded level spacing distribution, we show that in…
We challenge two foundational principles of localization physics by analyzing conductance fluctuations in two dimensions with unprecedented precision: (i) the Thouless criterion, which defines localization as insensitivity to boundary…
We present a new large-deviation approach to investigate the critical properties of the Anderson model on the Bethe lattice close to the localization transition in the thermodynamic limit. Our method allows us to study accurately the…
The single-impurity Anderson model has been the focus of theoretical studies of molecular junctions and the single-electron transistor, a nanostructured device comprising a quantum dot that bridges two otherwise decoupled metallic leads.…
The location of the mobility edge is a long standing problem in Anderson localization. In this paper, we show that the effective confining potential introduced in the localization landscape (LL) theory predicts the onset of delocalization…
We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the Power-law Banded Random Matrix (PBRM) model at criticality. Within a scattering…
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…