Related papers: On the absolutely continuous spectrum in a model o…
We show that a large class of limit-periodic Schr\"odinger operators has purely absolutely continuous spectrum in arbitrary dimensions. This result was previously known only in dimension one. The proof proceeds through the non-perturbative…
In this paper, we study the topological spectrum of weighted Birkhoff averages over aperiodic and irreducible subshifts of finite type. We show that for a uniformly continuous family of potentials, the spectrum is continuous and concave…
We characterize all bounded Hankel operators $\Gamma $ such that $\Gamma^*\Gamma$ has finite spectrum. We identify spectral data corresponding to such operators and construct inverse spectral theory including the characterization of these…
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…
We introduce two-parameter classes of exactly-solvable novel systems whose Hamiltonian operators could be represented by tridiagonal symmetric matrices in some orthogonal bases. The associated wavefunction is written as point-wise…
We consider a $2 \times 2$ operator matrix ${\mathcal A}_\mu,$ $\mu>0$ related with the lattice systems describing two identical bosons and one particle, another nature in interactions, without conservation of the number of particles. We…
We study the spectral properties of discrete one-dimensional Schr\"odinger operators with Sturmian potentials. It is shown that the point spectrum is always empty. Moreover, for rotation numbers with bounded density, we establish purely…
In this paper we develop the method of double operator integrals to prove trace formulae for functions of contractions, dissipative operators, unitary operators and self-adjoint operators. To establish the absolute continuity of spectral…
We show that, for the $C_0$-semigroups of scalar type spectral operators, a well-known necessary condition for the generation of eventually norm-continuous $C_0$-semigroups, formulated exclusively in terms of the location of the spectrum of…
We consider a $2\times2$ block operator matrix ${\mathcal A}_\mu$ $($$\mu>0$ is a coupling constant$)$ acting in the direct sum of one- and two-particle subspaces of a bosonic Fock space. The location of the essential spectrum of ${\mathcal…
Let $\mathcal{A}_1$ and $\mathcal{A}_2$ be standard operator algebras on complex Banach spaces $X_1$ and $X_2$, respectively. For $k\geq2$, let $(i_1,...,i_m)$ be a sequence with terms chosen from $\{1,\ldots,k\}$, and assume that at least…
In this paper, we develop the radial transfer matrix formalism for unitary one-channel operators. This generalizes previous formalisms for CMV matrices and scattering zippers. We establish an analog of Carmona's formula and deduce criteria…
We derive the spectrum of the Dirac operator for the linear sigma-model with quarks in the large N_c approximation using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear term…
We consider self-adjoint unbounded Jacobi matrices with diagonal q_n=n and weights \lambda_n=c_n n, where c_n is a 2-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum is…
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 $t$.…
The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…
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 consider discrete one-dimensional random Schroedinger operators with decaying matrix-valued, independent potentials. We show that if the l^2-norm of this potential has finite expectation value with respect to the product measure then…
I prove that quasi-periodic Schr\"odinger operators in arbitrary dimension have some absolutely continuous spectrum.
We consider Schr\"odinger operators $H=-\Delta+V({\mathbf x})$ in ${\mathbb R}^d$, $d\geq2$, with quasi-periodic potentials $V({\mathbf x})$. We prove that the absolutely continuous spectrum of a generic $H$ contains a semi-axis…