相关论文: The Spectrum and the Spectral Type of the Off-Diag…

We prove that dynamically defined Jacobi and CMV matrices associated with generic continuous sampling functions have all gaps predicted by the Gap Labelling Theorem open. We also give a mechanism for generic gap opening for quasi-periodic…

The discrete spectrum of complex banded matrices which are compact perturbations of the standard banded matrix of order $p$ is under consideration. The rate of stabilization for the matrix entries sharp in the sense of order which provides…

We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a…

We give the first example of a connected 4-regular graph whose Laplace operator's spectrum is a Cantor set, as well as several other computations of spectra following a common ``finite approximation'' method. These spectra are simple…

We consider a semi-periodic two-dimensional Schr\"odinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure. We prove that in the…

We consider Schr\"odinger operators with ergodic potential $V_\omega(n)=f(T^n(\omega))$, $n \in \Z$, $\omega \in \Omega$, where $T:\Omega \to \Omega$ is a non-periodic homeomorphism. We show that for generic $f \in C(\Omega)$, the spectrum…

A set $\Omega$, of Lebesgue measure 1, in the real line is called spectral if there is a set $\Lambda$ of real numbers such that the exponential functions $e_\lambda(x) = \exp(2\pi i \lambda x)$ form a complete orthonormal system on…

We present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes $n\times n$ zero-diagonal Jacobi matrices employed as its initial condition. This o.d.e.\ features a right-hand side with a…

We consider a class of singular, zero-range perturbations of the Hamiltonian of a quantum system composed by a test particle and a harmonic oscillators in dimension one, two and three and we study its spectrum. In facts we give a detailed…

We explore to what extent the relation between the absolute continuous spectrum and non-existence of subordinate generalized eigenvectors, known for scalar Jacobi operators, can be formulated also for block Jacobi operators with…

We consider the Schr\"odinger operator on the zigzag and armchair nanotubes (tight-binding models) in a uniform magnetic field $\mB$ and in an external periodic electric potential. The magnetic and electric fields are parallel to the axis…

Observable states are gauge-invariant. In a non-Abelian gauge theory, these are necessarily composite operators. We investigate the spectrum of these operators in the two-Higgs-doublet model. For this purpose, we are working along the lines…

The spectrum of three-diagonal self-adjoint $p$-periodic Jacobi matrix with positive off-diagonal elements $a_n$ an real diagonal elements $b_n$ consist of intervals separated by $p-1$ gaps $\gamma_i$, where some of the gaps can be…

We consider half-line Dirac operators with operator data of Wigner-von Neumann type. If the data is a finite linear combination of Wigner-von Neumann functions, we show absence of singular continuous spectrum and provide an explicit set…

We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a nontrivial singular continuous part. A new local Borg--Marchenko…

We analyse spectral properties of a class of compact perturbations of block Toeplitz operators associated with analytic symbols. In particular, a limiting absorption principle and the absence of singular continuous spectrum are shown. The…

Fermi surfaces are basic objects in solid state physics and in the spectral theory of periodic operators. We define several measures connected to Fermi surfaces and study their measure theoretic properties. From this we get absence of…

We numerically study energy spectra and localization properties of the double exchange model at irrational filling factor. To obtain variational ground state, we use a mumerical technique in momentum space by ``embedded'' boundary condition…

We consider the trace map associated with the Fibonacci Hamiltonian as a diffeomorphism on the invariant surface associated with a given coupling constant and prove that the non-wandering set of this map is hyperbolic if the coupling is…

A network is a countable, connected graph X viewed as a one-complex, where each edge [x,y]=[y,x] (x,y in X^0, the vertex set) is a copy of the unit interval within the graph's one-skeleton X^1 and is assigned a positive conductance c(xy). A…