The Aharonov−Bohm Effect

Harmonic oscillator in an elastic medium with a spiral dislocation

“…By comparing the effects that stems from the presence of the spiral dislocation with the screw dislocation discussed in Ref. [7], we have seen that no change in the angular momentum is given by the topological effects of the spiral dislocation, therefore, no Aharonov-Bohm-type effect for bound states [33] can be observed.…”

“…Two contributions to the energy levels arises from the topological effects of the spiral dislocation, where one of them is given by the presence of a fixed effective radius, ρ 0 = r 2 0 + β 2 , in the energy levels. Besides, no contribution to the angular momentum is given by the topology of the spiral dislocation, hence, there is no Aharonov-Bohm-type effect for bound states [33].…”

“…[16,23,26] (where the topology of the screw dislocation also modifies the angular momentum), we have that the effects of the topology of the spiral dislocation on the energy levels (11) yield no change in the angular momentum quantum number. In this sense, there is no Aharonov-Bohm-type effect for bound states [7,21,33].…”

“…[7], where the presence of the screw dislocation modifies the angular momentum [34] and gives rise to an Aharonov-Bohm-type effect for bound states [33], the presence of the spiral dislocation (an edge dislocation) gives no contribution to the angular momentum quantum number in the energy levels. In this sense, there is no Aharonov-Bohm-type effect for bound states [7,21,33]. Note that, by taking β = 0 in Eq.…”

Alternative Expression for the Electromagnetic Lagrangian

“…If we have two charged particles, for instance, we can say that the charge of each particle modifies the electromagnetic field configuration around it and that this field acts locally in the charge of the other particle causing a force. But with the prediction [1] and observation [2][3][4][5][6][7][8][9] of the Aharonov-Bohm (AB) effect, in which the interference pattern of charged quantum particles is affected by the electromagnetic field configuration even if they do not interact locally with these fields, the local interaction between charges and fields lost its generality in the description of electromagnetic phenomena.…”