The presence of chiral modes on the edges quantum Hall samples is essential to our understanding effect. In particular, these edge should support ballistic transport and therefore, in a single particle picture, be supported absolutely continuous spectrum single-particle Hamiltonian. We show this note that if free fermion system two-dimensional lattice gapped bulk, has nonvanishing conductance, ...

a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

We analyze the spectrum of the generalized Schrödinger operator in L2(Rν), ν ≥ 2, with a general local, rotationally invariant singular interaction supported by an infinite family of concentric, equidistantly spaced spheres. It is shown that the essential spectrum consists of interlaced segments of the dense point and absolutely continuous character, and that the relation of their lengths at hi...

We consider discrete one-dimensional Schrr odinger operators with quasi-Sturmian potentials. We present a new approach to the trace map dy-namical system which is independent of the initial conditions and establish a characterization of the spectrum in terms of bounded trace map orbits. Using this, it is shown that the operators have purely singular continuous spectrum and their spectrum is a C...

The spectrum of the Schrödinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any enlargement of the waveguide produces eigenvalues beneath the continuous spectrum [BGRS]. Also if the waveguide is bent eigenvalues will arise below the continuous spectrum [DE]. In this paper a magnetic field is added into the system. The spectrum of the magnetic Schrödinger...