Dirac oscillator in noncommutative space

We study the Dirac oscillator problem in the presence of the Aharonov-Bohm effect with the harmonic potential in commutative and noncommutative spaces in S = V and S =-V symmetry limits. We calculate exact energy levels and the corresponding eigenfunctions by the Nikiforov-Uvarov(NU) method and report the impact of the spin and the magnetic flux on the problem. Helpful numerical data is included.     

Is the Static Magnetic Vector Potential Screened by a Thick Superconducting Shield

In 1986 Tonomura and his co-workers reported the results of a test for the existence of the magnetic Aharonov-Bohm (AB) effect using permalloy toroids with a superconducting niobium coating. Classical Maxwell theory suggests that the group may have been able to observe the AB effect only because their superconducting shield was quite thin (2.5 penetration depths), and that, had a very thick shield been used, no AB effect would have been observable. However, orthodox quantum mechanics predicts that a static vector potential penetrates a superconducting shield of any thickness in cases where the magnetic flux inside the sample is an odd integer times h/2e. Regardless of which view is correct, it is argued in this paper that a superconductor only screens leakage or fringing field to the extent that it screens vector potential, so that there are doubts that the experiment answered the critics of earlier experiments, as was claimed.     

The double slit experiment,the Aharonov-Bohm effect,and a new quantum potential theory: Towards a realistic interpretation of quantum mechanics

In this paper, a new proposal of the quantum potential theory is presented, along with a discussion of the two-slit interference experiment and the Aharonov-Bohm effect, which are explicitly calculated within the scheme adopted. The present formulation holds the notion of particle trajectory and follows the interpretation suggested by de Broglie and Bohm, the quantum potential being a manifestation of the quantum wave. This wave always satisfies the Schrödinger equation and is considered as areal and separate entity from the particle with which is associated. In our approach we try to circumvent some conceptual difficulties that prevent the de Broglie-Bohm's theory from fulfilling a complete objective program. New effects are predicted, specially for the Aharonov-Bohm experiment in the regime of high magnetic fields, and a setup for their detection is proposed.     

Dirac Particle in an Aharonov-Bohm Potential: The Structure of the First Order S-matrix

The structure of the interaction Hamiltonian in the first order S-matrix element of a Dirac particle in an Aharonov-Bohm (AB) field is analyzed and shown to have interesting interesting algebraic properties. It is demonstrated that as a consequence of these properties, this interaction Hamiltonian splits both the incident and outgoing waves in the the first order components (eigenstates of the third component of the spin). The matrix element can then be viewed as the sum of two transitions taking place in these two channels of the spin. At the level of partial waves, each partial wave of the conserved total angular momentum is split into two partial waves of the orbital angular momentum in a manner consistent with the conservation of the total angular momentum quantum number.     

Topological insulator nanostructures and devices

Topological insulators＇ properties and their potential device applications are reviewed. We also explain why topologi- cal insulator （TI） nanostructnres are an important avenue for research and discuss some methods by which TI nanostructures are produced and characterized. The rapid development of high-quality TI nanostructures provides an ideal platform to ex- ploit salient physical phenomena that have been theoretically predicted but not yet experimentally realized.     

Resonance free regions in magnetic scattering by two solenoidal fields at large separation

We consider the problem of quantum resonances in magnetic scattering by two solenoidal fields at large separation in two dimensions. This system has trapped trajectories oscillating between two centers of the fields. We give a sharp lower bound on resonance widths when the distance between the two centers goes to infinity. The bound is described in terms of backward amplitudes calculated explicitly for scattering by each solenoidal field. The study is based on a new type of complex scaling method. As an application, we also discuss the relation to semiclassical resonances in scattering by two solenoidal fields.     

The conductance of the asymmetric Aharonov-Bohm ring with a delta-potential barrier in the presence of Rashba spin-orbit interaction

This Letter deals with the effect of a delta-potential barrier on the one-dimensional and asymmetric Aharonov-Bohm ring with Rashba spin-orbit interaction. The analytic expressions of the transmission amplitude and conductance are derived by applying the transfer matrix method in the one-electron scattering formalism. Resorting to an adequate tuning of the Aharonov-Bohm magnetic flux and Rashba coupling strength, a control of the conductance can be done by varying the strength and the location of the barrier. This may be useful in the design of further mesoscopic spin filters by using suitable asymmetry configurations.     

Optical analogue of the Aharonov-Bohm effect using anisotropic media

We show that in the context of paraxial optics, which can be analyzed through a wave equation similar to the non-relativistic Schrödinger equation of quantum mechanics but replacing time t by spatial coordinate z, the existence of a vector potential A_⊥ mimicking the magnetic vector potential in quantum mechanics is allowed by specific gauge symmetries of the optical field in a medium with anisotropic refractive index. In this way, we use Feynman?s path integral to demonstrate an optical analogue of the quantum-mechanical Aharonov-Bohm effect, encouraging the search for another optical systems with analogies with more complex quantum field theories.