The (3+1)-dimensional Dirac equation with position dependent mass in 4-vector electromagnetic fields is considered. Using two over-simplified examples (the Dirac-Coulomb and Dirac-oscillator fields), we report energylevels crossing as a spectral property or as an effect of the hidden supersymmetric quantum mechanical language and/or quasi-parity signatures. Under different settings of the relat...

This paper deals with functional equations in the form of $$f(x) + g(y) = h(x,y)$$ where h is given and f g are unknown. We will show that if a Borel measurable function associated characterizations uniform or Cauchy distributions, then there no solutions equation. Our proof uses characterization Dirac measure it also applicable to arctan

The DIRAC experiment, a magnetic double arm spectrometer, aims to measure the π + π − atom lifetime with 10% precision, using the high intensity 24 GeV/c proton beam of the CERN Proton Synchrotron. Since the value of this lifetime of order 10 s is dictated by strong interaction at low energy, a precise measurement of this quantity enables to study characteristic pion parameters in detail and to...

This paper introduces a numerical algorithm to compute the L2 optimal transport map between two measures μ and ν, where μ derives from a density ρ defined as a piecewise linear function (supported by a tetrahedral mesh), and where ν is a sum of Dirac masses. I first give an elementary presentation of some known results on optimal transport and then observe a relation with another problem (optim...

We study a classical model of helium atom in which, in addition to the Coulomb forces, the radiation reaction forces are taken into account. This modification brings in the model a new qualitative feature of a global character. Indeed, as pointed out by Dirac, in any model of classical electrodynamics of point particles involving radiation reaction one has to eliminate, from the a priori concei...

We discuss the weak coupling expansion of massless QCD with the Dirac operator which is derived by Neuberger based on the overlap formalism and satisfies the Ginsparg-Wilson relation. The axial U(1) anomaly associated to the chiral transformation proposed by Lüscher is calculated as an application and is shown to have the correct form of the topological charge density for perturbative backgroun...

We prove that limit-periodic Dirac operators generically have spectra of zero Lebesgue measure and a dense set them Hausdorff dimension. The proof combines ideas Avila from Schrödinger setting with new commutation argument for generating open spectral gaps. This overcomes an obstacle previously observed in the literature; namely, Schrödinger-type settings, translation corresponds to small L?-pe...

Title of Document: ELECTRONIC TRANSPORT IN DIRAC MATERIALS: GRAPHENE AND A TOPOLOGICAL INSULATOR(Bi2Se3) Sungjae Cho, Doctor of Philosophy, 2011 Directed By: Professor, Michael S. Fuhrer, Department of Physics Materials with Dirac electronic spectra (“Dirac materials”) have attracted much interest since the first successful electronic transport measurement in graphene in 2004. Dirac quasipartic...

Given a Dirac subbundle and an isotropic subbundle, we provide a canonical method to obtain a new Dirac subbundle. When the original Dirac subbundle is Courant involutive this construction has interesting applications, unifying and generalizing some results on the reduction of Dirac structures previously found in the literature.