Related papers: Spectral and Localization Properties for the One-D…
We carry out the spectral analysis of singular 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 perturbations, we…
Spectral properties and the confinement phenomenon for the coupling $H+V$ are studied, where $H=-i\alpha\cdot\nabla +m\beta$ is the free Dirac operator in $\mathcal{R}^3$ and $V$ is a measure-valued potential. The potentials $V$ under…
The Dirac equation may be thought as originating from a theory of five-dimensional (5D) space-time. We define a special 5D Clifford algebra and introduce a spin-1/2 constraint equation to describe null propagation in a 5D space-time…
We show that the energy spectrum of the one-dimensional Dirac equation in the presence of a spatial confining point interaction exhibits a resonant behavior when one includes a weak electric field. After solving the Dirac equation in terms…
In this paper, we prove pure point spectrum for a large class of Schr\"odinger operators over circle maps with conditions on the rotation number going beyond the Diophantine. More specifically, we develop the scheme to obtain pure point…
A coordinate system is constructed for a general accelerating observer in 1+1 dimensions, and is used to determine the particle density of the massless Dirac vacuum for that observer. Equations are obtained for the spatial distribution and…
We prove exponential and dynamical localization for the Schr\"odinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of…
The Dirac equation for a massive spin-1/2 field in a central potential V in three dimensions is studied without fixing a priori the functional form of V. The second-order equations for the radial parts of the spinor wave function are shown…
For a Dirac operator with non-local potential on a finite segment, a method of reconstruction of non-local potential from the spectral data is developed. Description of spectral data for such class of operators is given.
We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of m complex-valued half-densities over a connected compact n-dimensional manifold without boundary. The eigenvalues of the principal symbol are…
We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations…
We study the period doubling renormalization operator for dynamics which present two coupled laminar regimes with two weakly expanding fixed points. We focus our analysis on the potential point of view, meaning we want to solve…
We exhibit d-dimensional limit-periodic Schrodinger operators that are uniformly localized in the strongest sense possible. That is, for each of these operators, there is a uniform exponential decay rate such that every element of the hull…
We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are…
We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis,…
We present a result of localization for a matrix-valued Anderson-Bernoulli operator, acting on $L^2(\R)\otimes \R^N$, for an arbitrary $N\geq 1$, whose interaction potential is generic in the real symmetric matrices. For such a generic real…
Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac…
In this paper, we show the that the ground state energy of the one dimensional Discrete Random Schroedinger Operator with Bernoulli Potential is controlled asymptotically as the system size N goes to infinity by the random variable \ell_N,…
We argue that massless Dirac particles in two spatial dimensions with $1/r$ Coulomb repulsion and quenched random gauge field are described by a manifold of fixed points which can be accessed perturbatively in disorder and interaction…
Using a unified approach employing a homogeneous Lippmann-Schwinger-type equation satisfied by resonance functions and basic facts on Riesz potentials, we discuss the absence of threshold resonances for Dirac and Schrodinger operators with…