Quantum motion of a spinless particle in curved space: A viewpoint of scattering theory

In this work, we study the scattering of a spinless charged particle constrained to move on a curved surface in the presence of the Aharonov-Bohm potential. We begin with the equations of motion for the surface and transverse dynamics previously obtained in the literature (Ferrari G. and Cuoghi G., Phys. Rev. Lett. \textbf{100}, 230403 (2008)) and describe the surface with non-trivial curvature in terms of linear defects such as dislocations and disclinations. Expressions for the modified phase shift, S--matrix and scattering amplitude are determined by applying a suitable boundary condition at the origin, which comes from the self-adjoint extension theory. We also discuss the presence of a bound state obtained from the pole of the S--matrix. Finally, we claim that the bound state, the additional scattering and the dependence of the scattering amplitude with energy are solely due to the curvature effects.Comment: 9 pages, 1 figur

Inertial-Hall effect: the influence of rotation on the Hall conductivity

Inertial effects play an important role in classical mechanics but have been largely overlooked in quantum mechanics. Nevertheless, the analogy between inertial forces on mass particles and electromagnetic forces on charged particles is not new. In this paper, we consider a rotating non-interacting planar two-dimensional electron gas with a perpendicular uniform magnetic field and investigate the effects of the rotation in the Hall conductiv

On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries

The Dirac equation with both scalar and vector couplings describing the dynamics of a two-dimensional Dirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of the spin and the pseudo-spin symmetries. We analyze the presence of cylindrical symmetric scalar potentials which allows us to provide analytic solutions for the resultant field equation. By using an appropriate ansatz, we find that the radial equation is a biconfluent Heun-like differential equation. The solution of this equation provides us with more than one expression for the energy eigenvalues of the oscillator. We investigate these energies and find that there is a quantum condition between them. We study this condition in detail and find that it requires the fixation of one of the physical parameters involved in the problem. Expressions for the energy of the oscillator are obtained for some values of the quantum number $n$. Some particular cases which lead to known physical systems are also addressed.Comment: 15 pages, 8 figures, matches published versio

Assessing the Harvest Maturity of Brazilian Mangoes

No clear criterion exists to determine the optimum time to harvest mango. Some empirical relations are used to assess maturity, such as shoulder development. Moreover, as a result of the typical growing conditions in tropical climates, a huge variation in maturity and ripeness exists, seriously hampering the export of fruit in the global chain. The consequence for consumers in western countries is that sometimes mangoes are overripe at the retailer, or have to be kept for several days, even weeks, to reach the edible state, provided they do not rot in the meantime. To ensure an edible quality, the chlorophyll content in the fruit flesh, measured at harvest by Time-resolved Reflectance Spectroscopy (TRS), could be used as a maturity criterion for mango fruit. Commercially grown fruit were harvested in Brazil and transported to Italy by plane. Fruits were measured using TRS at 630 nm for absorption coefficient (µa) and skin colour. The development of µa was followed on 60 fruits during 15 days of storage at 20°C. The remainders of fruit were used to measure firmness destructively. Absorption coefficient decreased during shelf life according to a logistic pattern, as expected for colour development. Taking the variation between the individual fruit into account, 72% of the variation was accounted for. Nevertheless, µa assessed at harvest could be converted into a biological shift factor (BSF), as an expression of the maturity at harvest of each individual fruit. This biological shift factor explained about 70% of the variation in firmness development in individual fruit. These preliminary results indicate that TRS methodology coupled with BSF theory could be useful in assessing maturity at harvest and assuring acceptable eating quality of mango