相关论文: Localisation of Geometric Anisotropy

Scaling of the conductances and the finite-size localization lengths is generalized to anisotropic systems and tested in two dimensional systems. Scaling functions of isotropic systems are recovered once the dimension of the system in each…

Our previous results [J.Phys.: Condens. Matter 14 (2002) 13777] dealing with the analytical solution of the two-dimensional (2-D) Anderson localization problem due to disorder is generalized for anisotropic systems (two different hopping…

We refine a recently-proposed class of local entropic loss functions by restricting the smoothening regularization to only a subset of weights. The new loss functions are referred to as partial local entropies. They can adapt to the…

The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic…

Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic…

Besides the chemical constituents, it is the lattice geometry that controls the most important material properties. In many interesting compounds, the arrangement of elements leads to pronounced anisotropies, which reflect into a varying…

We study Anderson localization of a scalar wave in an ensemble of resonant point scatterers embedded in an anisotropic background medium. For uniaxial anisotropy of moderate strength, the mobility edges and the critical exponent of the…

Bifractal is a highly anisotropic structure where planar fractals are stacked to form a 3-dimensional lattice. The localization lengths along fractal structure for the Anderson model defined on a bifractal are calculated. The critical…

We investigate localization properties in the highly anisotropic and intrinsically disordered layered material, which is analogous to high-Tc cuprates. By varying the anisotropy of the system which is parameterized by the interlayer hopping…

We consider a system of two discrete quasiperiodic 1D particles as an operator on $\ell^2(\mathbb Z^2)$ and establish Anderson localization at large disorder, assuming the potential has no cosine-type symmetries. In the presence of…

We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a target region and a tolerance, the algorithm identifies candidate eigenpairs for which…

We characterize the geometrical and topological aspects of a dynamical system by associating a geometric phase with a phase space trajectory. Using the example of a nonlinear driven damped oscillator, we show that this phase is resilient to…

The topology of an insulator can be defined even when all eigenstates of the system are localized - an extreme case of Anderson insulators that we call ultra-localized. We derive the classification of such ultra-localized insulators in all…

We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…

Several phenomena related to the critical behaviour of non-interacting electrons in a disordered 2d tight-binding system with a magnetic field are studied. Localization lengths, critical exponents and density of states are computed using…

In this paper, we present a family of multivariate grid transfer operators appropriate for anisotropic multigrid methods. Our grid transfer operators are derived from a new family of anisotropic interpolatory subdivision schemes. We study…

We introduce a new 2N--parametric family of maximally superintegrable systems in N dimensions, obtained as a reduction of an anisotropic harmonic oscillator in a 2N--dimensional configuration space. These systems possess closed bounded…

We establish the stable homotopy classification of elliptic pseudodifferential operators on manifolds with corners and show that the set of elliptic operators modulo stable homotopy is isomorphic to the K-homology group of some stratified…

A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for…

We obtain a classification of elliptic operators modulo stable homotopy on manifolds with edges (this is in some sense the simplest class of manifolds with nonisolated singularities). We show that the operators are classified by the…