Aharonov-Bohm scattering on a cone

Abstract

The Aharonov-Bohm scattering amplitude is calculated in the context of planar gravity with localized sources which also carry a magnetic flux. These sources cause space-time to develop conical singularities at their location, thus introducing novel effects in the scattering of electrically charged particles. The behaviour of the wave function in the proximity of the classical scattering directions is analyzed by means of an asymptotic expansion previously introduced by the author. It is found that, in contrast with the Aharonov-Bohm effect in flat space, integer values of the numerical flux can produce observable effects.

Hidden superconformal symmetry of the spinless Aharonov–Bohm system

“…It does not contradict the self-adjointness of Q AB α , the supercharge can be diagonalized with making use of its eigenstates (2. 19) and (2.20). Hence, the supercharges annihilate just one half of the zero-energy states.…”

“…Hence, the eigefunctions Φ λ,l = φ 2l e 2ilϕ + φ 2l−1 e i(2l−1)ϕ lying in these subspaces have exactly the same form as (2. 19) and (2.20). The situation is different in the subspace H l0 .…”

“…The AB effect underlies the dynamical realization of anyons [12][13][14], which are currently supposed to play the key role in the fractional Hall effect [15]. It appears in the analysis of cosmic strings [16,17], and planar gravity [18,19]. This effect also plays an important role in the physics of graphene and nanotubes [20][21][22].…”

Relativistic quantum scattering on a cone

“…Other situations connected with the effect of topology, electromagnetic flux or a combination of them can be found in related papers on the scattering off a magnetic string [7], magnetic flux string [9], chiral cosmic string [10] and a cosmic string within the framework of Kaluza-Klein theory [11].…”

Some effects on quantum systems due to the gravitational field of a topological defect

“…As examples of the influence of the topology on an atomic system, we can mention the studies concerning to quantum mechanics on a cone [5][6][7], the interaction of a quantum system with space-times generated by topological defects [8,9] and the modification of the energy levels of a hydrogen atom [3] placed in the gravitational field of a cosmic string [10].…”