Spectral analysis of non-local Schrödinger operators

The spectrum of non-local discrete Schrödinger operators with a δ-potential

The behaviour of the spectral edges (embedded eigenvalues and resonances) is discussed at the two ends of the continuous spectrum of non-local discrete Schrödinger operators with a δ-potential. These operators arise by replacing the discrete Laplacian by a strictly increasing C1-function of the discrete Laplacian. The dependence of the results on this function and the lattice dimension are expl...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Isometries, Fock Spaces, and Spectral Analysis of Schrödinger Operators on Trees

We construct conjugate operators for the real part of a completely non unitary isometry and we give applications to the spectral and scattering theory of a class of operators on (complete) Fock spaces, natural generalizations of the Schrödinger operators on trees. We considerC∗-algebras generated by such Hamiltonians with certain types of anisotropy at infinity, we compute their quotient with r...

Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators

In this paper, we consider one dimensional adiabatic quasi-periodic Schrödinger operators in the regime of strong resonant tunneling. We show the emergence of a level repulsion phenomenon which is seen to be very naturally related to the local spectral type of the operator: the more singular the spectrum, the weaker the repulsion. Résumé. Dans cet article, nous étudions une famille d’opérateurs...

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...