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Register a new userPartial Wave Analysis of Scattering with Nonlocal Aharonov-Bohm Effect and Anomalous Cross Section induced by Quantum Interference
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De-Hone Lin
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Partial wave theory of a three dmensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a ``hard shere like potential and the magnetic flux is examined. An anomalous total cross section is revealed at the specific quantized magnetic flux at low energy which helps explain the composite fermion and boson model in the fractional quantum Hall effect. Since the nonlocal quantum interference of magnetic flux on the charged particles is universal, the nonlocal effect is expected to appear in quite general potential system and will be useful in understanding some other phenomena in mesoscopic phyiscs.
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Partial wave theory of a two dimensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a ``hard disk like potential and the magnetic flux is examined. Since the nonlocal influence of magnetic flux on the charged particles is universal, the nonlocal effect in hard disk case is expected to appear in quite general potential system and will be useful in understanding some phenomena in mesoscopic phyiscs.
In this work we consider a quantum variation of the usual Aharonov-Bohm effect with two solenoids sufficiently close one to the other so that (external) electron cannot propagate between two solenoids but only around both solenoids. Here magnetic field (or classical vector potential of the electromagnetic field) acting at quantum propagating (external) electron represents the quantum mechanical average value or statistical mixture. It is obtained by wave function of single (internal, quantum propagating within some solenoid wire) electron (or homogeneous ensemble of such (internal) electrons) representing a quantum superposition with two practically non-interfering terms. All this implies that phase difference and interference shape translation of the quantum propagating (external) electron represent the quantum mechanical average value or statistical mixture. On the other hand we consider a classical analogy and variation of the usual Aharonov-Bohm effect in which Aharonov-Bohm solenoid is used for the primary coil inside secondary large coil in the remarkable classical Faraday experiment of the electromagnetic induction.
In order to determine the origin of discontinuities which arise when the semiclassical propagator is employed to describe an infinitely long and infinitesimally thin solenoid carrying magnetic flux, we give a systematic derivation of the semiclassical limit of the motion of an otherwise free charged particle. Our limit establishes the connection of the quantum mechanical canonical angular momentum to its classical counterpart. Moreover, we show how a picture of Aharonov-Bohm interference of two half-waves acquiring Diracs magnetic phase when passing on either side of the solenoid emerges from the quantum propagator, and that the typical scale of the resulting interference pattern is fully determined by the ratio of the angular part of Hamiltons principal function to Plancks constant. The semiclassical propagator is recovered in the limit when this ratio diverges. We discuss the relation of our results to the whirling-wave representation of the exact propagator.
We study a system of electrons moving on a noncommutative plane in the presence of an external magnetic field which is perpendicular to this plane. For generality we assume that the coordinates and the momenta are both noncommutative. We make a transformation from the noncommutative coordinates to a set of commuting coordinates and then we write the Hamiltonian for this system. The energy spectrum and the expectation value of the current can then be calculated and the Hall conductivity can be extracted. We use the same method to calculate the phase shift for the Aharonov-Bohm effect. Precession measurements could allow strong upper limits to be imposed on the noncommutativity coordinate and momentum parameters $Theta$ and $Xi$.
Topological insulators have an insulating bulk but a metallic surface. In the simplest case, the surface electronic structure of a 3D topological insulator is described by a single 2D Dirac cone. A single 2D Dirac fermion cannot be realized in an isolated 2D system with time-reversal symmetry, but rather owes its existence to the topological properties of the 3D bulk wavefunctions. The transport properties of such a surface state are of considerable current interest; they have some similarities with graphene, which also realizes Dirac fermions, but have several unique features in their response to magnetic fields. In this review we give an overview of some of the main quantum transport properties of topological insulator surfaces. We focus on the efforts to use quantum interference phenomena, such as weak anti-localization and the Aharonov-Bohm effect, to verify in a transport experiment the Dirac nature of the surface state and its defining properties. In addition to explaining the basic ideas and predictions of the theory, we provide a survey of recent experimental work.
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