1,721,005 research outputs found
Sharp exponential decay for solutions of the stationary perturbed Dirac equation
No full textWe determine the largest rate of exponential decay at infinity for non-trivial solutions to the Dirac equation nψ + ψ = 0in Rn, being n the massless Dirac operator in dimension n ≥ 2 and a (possibly non-Hermitian) matrix-valued perturbation such that |(x)|∼|x|-at infinity, for-∞ < < 1. Also, we show that our results are sharp for n {2, 3}, providing explicit examples of solutions that have the prescripted decay, in presence of a potential with the related behavior at infinity. As a consequence, we investigate the exponential decay at infinity for the eigenfunctions of the perturbed massive Dirac operator, and determine the sharpest possible decay in the case that ≤ 0 and n {2, 3}
Boundary Triples for the Dirac Operator with Coulomb-Type Spherically Symmetric Perturbations
Full text linkWe determine explicitly a boundary triple for the Dirac operator in , for and , with . Consequently we determine all the self-adjoint realizations of in terms of the behaviour of the functions of their domain in the origin. When , we discuss the problem of selecting the distinguished extension requiring that its domain is included in the domain of the appropriate quadratic form
Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
Full text linkWe describe the self-adjoint realizations of the operator , for , and , for . We characterize the self-adjointness in terms of the behaviour of the functions of the domain in the origin, exploiting Hardy-type estimates and trace lemmas. Finally, we describe the distinguished extension.Istituto Italiano di Alta Matematica "F. Severi
Gaussian decay of harmonic oscillators and related models
Full text linkWe prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can produce solutions to the evolutionary Schrödinger flows associated to the Hamiltonians, with a stronger Gaussian decay at two distinct times. We then characterize, in a quantitative way, the sharpest possible Gaussian decay of solutions as a function of the oscillation frequency or the strength of the field, depending on the Hamiltonian which is considered. This is connected to the Hardy's Uncertainty Principle for free Schrödinger evolutions
A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator
Full text linkWe prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials of Coulomb type: we characterise its eigenvalues in terms of the Birman–Schwinger principle and we bound its discrete spectrum from below, showing that the ground-state energy is reached if and only if verifies some rigidity conditions. In the particular case of an electrostatic potential, these imply that is the Coulomb potential
Mass propagation for electromagnetic Schrödinger evolutions
No full textWe investigate the validity of Gaussian lower bounds for solutions to an electromagnetic Schrödinger equation with a bounded time-dependent complex electric potential and a time-independent vector magnetic potential. We prove that, if a suitable geometric condition is satisfied by the vector potential, then positive masses inside of a bounded region at a single time propagate outside the region, provided a suitable average in space–time cylinders is taken
Self-adjointness for the MIT bag model on an unbounded cone
Full text linkWe consider the massless Dirac operator with the MIT bag boundary conditions
on an unbounded three-dimensional circular cone. For convex cones, we prove
that this operator is self-adjoint defined on four-component --functions
satisfying the MIT bag boundary conditions. The proof of this result relies on
separation of variables and spectral estimates for one-dimensional fiber
Dirac-type operators. Furthermore, we provide a numerical evidence for the
self-adjointness on the same domain also for non-convex cones. Moreover, we
prove a Hardy-type inequality for such a Dirac operator on convex cones, which,
in particular, yields stability of self-adjointness under perturbations by a
class of unbounded potentials. Further extensions of our results to Dirac
operators with quantum dot boundary conditions are also discussed.Comment: 38 pages, 1 figure; revised versio
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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