Related papers: Spectrum of analytic continuation

The purpose of this paper is to prove that the spectrum of an isotropic Maxwell operator with electric permittivity and magnetic permeability that are periodic along certain directions and tending to a constant super-exponentially fast in…

We prove two extension theorems for positive maps from operator systems into matrix algebras

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

For positive $C_0$-semigroups $S$ and $T$ on a Banach lattice such that $S(t) \le T(t)$ for all times $t$, we prove that analyticity of $T$ implies analyticity of $S$. This answers an open problem posed by Arendt in 2004. Our proof is based…

We explore the relationship between lattice field theory and graph theory, placing special emphasis on the interplay between Dirac and scalar lattice operators and matrices within the realm of spectral graph theory. Beyond delving into…

We consider Schr\"odinger operators with periodic electric and magnetic potentials on periodic discrete graphs. The spectrum of such operators consists of an absolutely continuous (a.c.) part (a union of a finite number of non-degenerate…

We prove that the spectrum of the almost Mathieu operator is absolutely continuous if and only if the coupling is subcritical. This settles Problem 6 of Barry Simon's list of Schr\"odinger operator problems for the twenty-first century.

We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in…

Given a family of self-adjoint operators $(A_t)_{t\in T}$ indexed by a parameter $t$ in some topological space $T$, necessary and sufficient conditions are given for the spectrum $\sigma(A_t)$ to be Vietoris continuous with respect to $t$.…

We apply a method recently devised by one of the authors to obtain an approximate analytical formula for the spectrum of a quantum anharmonic potential. Due to its general features the method can be applied with minimal effort to general…

We suggest that a certain one-to-one parametrization of completely positive maps on the matrix algebra might be useful in the study of quantum channels. This is illustrated in the case of binary quantum channels. While the algorithm is…

We demonstrate a one-dimensional magnetic system can exhibit a Cantor-type spectrum using an example of a chain graph with $\delta$ coupling at the vertices exposed to a magnetic field perpendicular to the graph plane and varying along the…

We prove that the spectrum of a Schrodinger operator that is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous.

We show that for any $\lambda \in \mathbb{C}$ with $|\lambda|<1$ there exists an analytic expanding circle map such that the eigenvalues of the associated transfer operator (acting on holomorphic functions) are precisely the nonnegative…

Dirac operators in non-trivial topology backgrounds in a finite box are reviewed. We analyze how the formalism translates to the lattice, with special emphasis on uniform field backgrounds.

On an infinite set some closure operators are finitary (algebraic) while others are not. We can generalize this idea for a complete algebraic lattice letting the compact elements act as the finite sets. With this in mind, we will consider…

We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary…

We introduce a transfer matrix method for the spectral analysis of discrete Hermitian operators with locally finite hopping. Such operators can be associated with a locally finite graph structure and the method works in principle on any…

In this paper, we give the spectrum of a matrix by using the quotient matrix, then we apply this result to various matrices associated to a graph and a digraph, including adjacency matrix, (signless) Laplacian matrix, distance matrix,…

We derive a sharp criterion on the spectra of periodic discrete Schr\"odinger operators acting on connected periodic lattices: the measure of the spectrum goes to zero as the coupling constant goes to infinity if and only if there is no…