By James Hamilton
The Aharonov-Bohm impact is linked to cyclic movement. it truly is one in all a couple of anholonomic results, and which means the dynamical description is dependent upon the present place of the process and at the course in which it reached that place. An instance of an anholonomic influence is Foucault's recognized pendulum, which easily demonstrates the Earth's rotation. The Sagnac influence - a mild beam passing round a turned around procedure of mirrors - is one other instance. smooth dynamical advancements akin to Hannay's perspective and Berry's section are additional worthy examples.
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Extra info for Aharonov-Bohm and other Cyclic Phenomena
10; changing can thus be seen as a change in the boundary condition that the wave function must obey on going once around the surface of the solenoid. The situation is somewhat similar to the polarization of the vacuum around an atomic nucleus of charge +Ze. Changing Z will change the polarization whether or not any electron is present. The difference between the two cases is that it may be easier to envisage the electric field arising from the vacuum polarization, than it is to remember the difference between wave 48 5.
32 3. 20a). 2) ~(er A . 18a) we see that the change in phase of r once around the orbit is 2~rM' + -~e~(~r) A . 21) have been used. 21a) is (minus) the AB phase. 20c). 21a) thus show how, for different values of n, the total phase change 2~rA/h is made up of different proportions from the quantized term and the AB term. In each case the particle describes the same orbit p = PT, in induction Bz = B. In the extreme case of n --* oo, the AB term vanishes; while for n = 0, the quantized term vanishes.
30 3. Generalization of the Aharonov-Bohm Effect Similar phenomena can be observed in magneto-resistance experiments. For example a thin hollow metal cylinder encloses a narrow solenoid lying on the axis of the cylinder. The solenoid has magnetic flux ~. It is found that the electrical resistivity (along the cylinder) will oscillate with the period r as the flux is varied. For an account of resistivity oscillations see the article by A. G. Aronov and Yu. V. 8]. This article also contains an account of relevant experiments.