Related papers: Resonances for the radial Dirac operators
Several important observables, like the quark condensate and the Taylor coefficients of the expansion of the QCD pressure with respect to the chemical potential, are based on the trace of the inverse Dirac operator and of its powers. Such…
We examine spectra of Dirac operators on compact hyperbolic surfaces. Particular attention is devoted to symmetry considerations, leading to non-trivial multiplicities of eigenvalues. The relation to spectra of Maass-Laplace operators is…
In dimension $d\geq 3$, we give examples of nontrivial, compactly supported, complex-valued potentials such that the associated Schr\"odinger operators have no resonances. If $d=2$, we show that there are potentials with no resonances away…
This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric…
Energy resonance in scattering is usually investigated either directly in the complex energy plane (E-plane) or indirectly in the complex angular momentum plane (L-plane). Another formulation complementing these two approaches was…
The spectral properties of the pseudo-differential operator $(-d^2/dx^2)^{1/2}+x^2$ are analyzed by a combination of functional integration methods and direct analysis. We obtain a representation of its eigenvalues and eigenfunctions, prove…
We obtain new results about the high-energy distribution of resonances for the one-dimensional Schr\"odinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular…
For small perturbations of Minkowski space, we show that the square of the Lorentzian Dirac operator $P= -D^2$ has real spectrum apart from possible poles in a horizontal strip. Furthermore, for $\varepsilon>0$ we relate the poles of the…
In this paper, we prove the existence of the scattering operator for the fractional magnetic Schrodinger operators. For this, we construct the fractional distorted Fourier transforms with magnetic potentials. Applying the properties of the…
The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this…
We consider the light scattering from a pair of point-like electrical dipoles. Whenever the polarizability of each dipole violates the optical theorem, the response of the pair (both in far-field and near-field) exhibits exact resonances as…
The presence of resonances modifies the passage of light or of electrons through a disordered medium. We generalize random matrix theory to account for this effect. Using supersymmetry, we calculate analytically the mean density of states,…
We discuss resonances for Schr\"odinger operators on metric graphs which consists of a finite compact part and a finite number of halflines attached to it; the vertex coupling is assumed to be of the $\delta$-type or certain modifications…
We study scattering from potentials that rise monotonically on one side; this is generally avoided. We report that resonant states are absent in such potentials when they are smooth and single-piece having less than three real turning…
In this paper we show how rotational bands of resonances can be described by using trajectories of poles of the scattering amplitude in the complex angular momentum plane: each band of resonances is represented by the evolution of a single…
We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer…
A periodic layer of resonant scatterers is considered in the dipolar approximation. An asymptotic expression for the field diffracted is given in terms of an impedance operator. It is shown that surface Bloch modes appear as a collective…
We define Dirac operators on $\mathbb{S}^3$ (and $\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among…
In the paper, we give four different examples of the rescaled Dirac operator by the perturbation of the function f. Further, based on the trilinear Clifford multiplication by functional of differential one-forms, we compute the spectral…
In this article, we study the spectrum of the magnetic Dirac operator, and the magnetic Dirac operator with potential over complete Riemannian manifolds. We find sufficient conditions on the potentials as well as the manifold so that the…