Related papers: Anderson-like Transition for a Class of Random Spa…
We calculate the effective spatial dimension $d_\text{IR}$ of electron modes at critical points of 3D Anderson models in various universality classes (O,U,S,AIII). The results are equal within errors, and suggest the super-universal value…
The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type…
We present numerical results for the Rosenzweig Porter model for all symmetry classes of the Dyson threefold way. We analyzed the fluctuation properties in the eigenvalue spectra, and compared them with existing and new analytical results.…
Anderson localization is a universal phenomenon affecting non-interacting quantum particles in disorder. In three spatial dimensions it becomes particularly interesting to study because of the presence of a quantum phase transition from…
In the present note we show dynamical localization for an Anderson model with missing sites in a discrete setting at the bottom of the spectrum in arbitrary dimension $d$. In this model, the random potential is defined on a relatively dense…
The three-dimensional Anderson model represents a paradigmatic model to understand the Anderson localization transition. In this work we first review some key results obtained for this model in the past 50 years, and then study its…
We report on an anomalous behavior of the absorption spectrum in a one-dimensional lattice with long-range-correlated diagonal disorder with a power-like spectrum in the form S(k) ~ 1/k^A. These type of correlations give rise to a phase of…
A new approach is applied to the 1D Anderson model by making use of a two-dimensional Hamiltonian map. For a weak disorder this approach allows for a simple derivation of correct expressions for the localization length both at the center…
In this work, we prove a bound on multiplicity of the singular spectrum for certain class of Anderson Hamiltonians. The class of operator is $H^\omega=\Delta+\sum_{n\in\mathbb{Z}^d}\omega_n P_n$ on the Hilbert space $\ell^2(\mathbb{Z}^d)$,…
We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key…
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…
The Anderson transition between localized and metallic states is traditionally analyzed by assuming a one-parameter scaling hypothesis. Although that hypothesis has been confirmed near two dimensions by epsilon = d-2 expansion of the…
A novel tensor-based formula for solving the linear systems involving Kronecker sum is proposed. Such systems are directly related to the matrix and tensor forms of Sylvester equation. The new tensor-based formula demonstrates the…
We investigate the possibility of an Anderson transition below two dimensions in disordered systems of non-interacting electrons with symplectic symmetry. Numerical analysis of energy level statistics and conductance statistics on…
The Anderson-Mott transition of disordered interacting electrons is shown to share many physical and technical features with classical random-field systems. A renormalization group study of an order parameter field theory for the…
We investigate a variant of the parabolic Anderson model, introduced in previous work, in which an i.i.d.\! potential is partially duplicated in a symmetric way about the origin, with each potential value duplicated independently with a…
We consider a two dimensional magnetic Schroedinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove…
Anderson localization is a universal quantum feature caused by destructive interference. On the other hand chiral symmetry is a key ingredient in different problems of theoretical physics: from nonperturbative QCD to highly doped…
The two main results of the article are concerned with Anderson Localization for one-dimensional lattice Schroedinger operators with quasi-periodic potentials with d frequencies. First, in the case d = 1 or 2, it is proved that the spectrum…
Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…