Aharonov-Bohm oscillations in a quantum ring: Eccentricity and electric-field effects

The effects of an in-plane electric field and eccentricity on the electronic spectrum of a GaAs quantum ring in a perpendicular magnetic field are studied. The effective-mass equation is solved by two different methods: an adiabatic approximation and a diagonalization procedure after a conformal mapping. It is shown that the electric field and the eccentricity may suppress the Aharonov-Bohm oscillations of the lower energy levels. Simple expressions for the threshold energy and the number of flat energy bands are found. In the case of a thin and eccentric ring, the intensity of a critical field which compensates the main effects of eccentricity is determined. The energy spectra are found in qualitative agreement with previous experimental and theoretical works on anisotropic rings.

BERRY PHASE, AHARONOV-BOHM EFFECT AND TOPOLOGY

The Berry phase for an electron in a one-dimensional box rotated around a magnetic flux line has contributions from the geometry and the magnetic flux, which gives an Aharonov-Bohm effect. For a circular box enclosing the magnetic flux, the Berry phase depends on the boundary conditions.

Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfests theorem

The electron-diffraction pattern for two slits with magnetic flux confined to an inaccessible region between them is calculated. The Aharonov-Bohm effect gives a diffraction pattern that is asymmetric but has a symmetric envelope. In general, both the expected displacement and the kinetic momentum of the electron are nonzero as a consequence of the asymmetry. Nevertheless, Ehrenfests theorems and the conservation of momentum are satisfied. © 1992 The American Physical Society.

Aspects of classical and quantum motion on a flux cone

Motion of a nonrelativistic particle on a cone with a magnetic flux running through the cone axis (a flux cone) is studied. It is expressed as the motion of a particle moving on the Euclidean plane under the action of a velocity-dependent force. The probability fluid (quantum flow) associated with a particular stationary state is studied close to the singularity, demonstrating nontrivial Aharonov-Bohm effects. For example, it is shown that, near the singularity, quantum flow departs from classical flow. In the context of the hydrodynamical approach to quantum mechanics, quantum potential due to the conical singularity is determined, and the way it affects quantum flow is analyzed. It is shown that the winding number of classical orbits plays a role in the description of the quantum Bow. The connectivity of the configuration space is also discussed.

Gravitation: global formulation and quantum effects

A non-integrable phase-factor global approach to gravitation is developed by using the similarity of teleparallel gravity to electromagnetism. The phase shifts of both the COW and the gravitational Aharonov-Bohm effects are obtained. It is then shown, by considering a simple slit experiment, that in the classical limit the global approach yields the same result as the gravitational Lorentz force equation of teleparallel gravity. It represents, therefore, the quantum mechanical version of the classical description provided by the gravitational Lorentz force equation. As teleparallel gravity can be formulated independently of the equivalence principle, it will consequently require no generalization of this principle at the quantum level.

Selected topics in teleparallel gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Green functions of the Dirac equation with magnetic-solenoid field

Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2+1 and 3+1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as proper time integrals are derived. The nonrelativistic limit is considered. For the sake of completeness the Green functions of the Klein-Gordon particles are constructed as well. (C) 2004 American Institute of Physics.

THE PARAMETERS OF THE LEWIS METRIC FOR THE WEYL CLASS

We provide physical interpretation for the four parameters of the stationary Lewis metric restricted to the Weyl class. Matching this spacetime to a completely anisotropic, rigidly rotating, fluid cylinder, we obtain from the junction conditions that one of these parameters is proportional to the vorticity of the source. From the Newtonian approximation a second parameter is found to be proportional to the energy per unit of length. The remaining two parameters may be associated to a gravitational analog of the Aharanov-Bohm effect. We prove, using the Cartan scalars, that the Weyl class metric and static Levi-Civita metric are locally equivalent, i.e., indistinguishable in terms of its curvature.

Dirac equation in magnetic-solenoid field

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Quantum rings of arbitrary shape and non-uniform width in a threading magnetic field

The electronic states of quantum rings with centerlines of arbitrary shape and non-uniform width in a threading magnetic field are calculated. The solutions of the Schrodinger equation with Dirichlet boundary conditions are obtained by a variational separation of variables in curvilinear coordinates. We obtain a width profile that compensates for the main effects of the curvature variations in the centerline. Numerical results are shown for circular, elliptical, and limacon-shaped quantum rings. We also show that smooth and tiny variations in the width may strongly affect the Aharonov-Bohm oscillations.

Probing the antisymmetric Fano interference assisted by a Majorana fermion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multimessenger search for sources of gravitational waves and high-energy neutrinos: Initial results for LIGO-Virgo and IceCube

We report the results of a multimessenger search for coincident signals from the LIGO and Virgo gravitational-wave observatories and the partially completed IceCube high-energy neutrino detector, including periods of joint operation between 2007-2010. These include parts of the 2005-2007 run and the 2009-2010 run for LIGO-Virgo, and IceCube's observation periods with 22, 59 and 79 strings. We find no significant coincident events, and use the search results to derive upper limits on the rate of joint sources for a range of source emission parameters. For the optimistic assumption of gravitational-wave emission energy of 10(-2) M(circle dot)c(2) at similar to 150 Hz with similar to 60 ms duration, and high-energy neutrino emission of 1051 erg comparable to the isotropic gamma-ray energy of gamma-ray bursts, we limit the source rate below 1.6 x 10(-2) Mpc(-3) yr(-1). We also examine how combining information from gravitational waves and neutrinos will aid discovery in the advanced gravitational-wave detector era.

Formalismo canônico da mecânica clássica: alicerce da mecânica quântica

We present a succinct review of the canonical formalism of classical mechanics, followed by a brief review of the main representations of quantum mechanics. We emphasize the formal similarities between the corresponding equations. We notice that these similarities contributed to the formulation of quantum mechanics. Of course, the driving force behind the search of any new physics is based on experimental evidence

Combined measurement of the Higgs Boson Mass in pp collisions at root s=7 and 8 TeV with the ATLAS and CMS experiments

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Interferência Fano antissimétrica assistida por um férmion de Majorana

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)