It is shown that the complete localization of eigenvectors for the almost Mathieu operator entails the absence of Cantor spectrum for this operator.

It is reported a combined numerical approach to study the localization properties of the one-dimensional tight-binding model with potential modulated along the prime numbers. A localization-delocalization transition was found as function of the potential intensity; it is also argued that there are delocalized states for any value of the potential intensity. PACS numbers: 03.65.-w, 72.20.Ee, 72....

Iris recognition is regarded as the most reliable and accurate biometric identification system. Most commercial iris recognition systems use patented algorithms developed by Daugman and these algorithms are able to produce perfect recognition rates. These algorithms are based on linear search methods which make the identification process extremely slow and also raise the false acceptance rate b...

The set of continuous norm-preserving stochastic Schrödinger equations associated with the Lindblad master equation is introduced. This set is used to describe the localization properties of the state vector toward eigenstates of the environment operator. Particular focus is placed on determining the stochastic equation which exhibits the highest rate of localization for wide open systems. An e...

The localization of the essential spectrum of a relativistic twoelectron ion is provided. The analysis is performed with the help of the pseudorelativistic Brown-Ravenhall operator which is the restriction of the CoulombDirac operator to the electrons’ positive spectral subspace.

This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a product of a deterministic unitary oper...

We study a semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. Key results are semiboundedness theorem of the Schrödinger operator, Laplace-type asymptotic formula and IMS localization formula. We also make a remark on semiclassical problem of a Schrödinger operator on a path space over a Riemannian manifold. MSC: Primary 81Q20, Secondary 60H07, 35J10.