Aharonov-Bohm and other Cyclic Phenomena by James Hamilton

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By James Hamilton

The Aharonov-Bohm impression is linked to cyclic movement. it really is considered one of a few anholonomic results, and which means the dynamical description is dependent upon the present place of the process and at the course wherein it reached that place. An instance of an anholonomic impact is Foucault's recognized pendulum, which easily demonstrates the Earth's rotation. The Sagnac impact - a gentle beam passing round a circled process of mirrors - is one other instance. smooth dynamical advancements similar to Hannay's attitude and Berry's part are additional necessary examples.

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1. When the electron, on path 1 (Fig. 6a) 2~r dz T h e effect on path 2 is numerically the reverse, and in each case we have to nse ~0 = lr. At this point Pryce goes over to wave mechanics. 2b) for the behaviour in the plane z = 0 [with 9 = ~ ( z = 0)]. On a plane x = - / w h i c h lies just beyond the whisker (and on the same side as O) in Fig. 6b) while the wave packet on path 2 gets the opposite extra phase. 7) On the observing plane x = 0 there is a trivial complication arising from the amplification factor co/bo mentioned above.

13) shows t h a t an expression analogous to the AB term is an integral part of any simple description of the asymmetrical motion of a charged particle in an induction field. The fact t h a t A, the component of angular momentum about Oz, is not constant for motion in the induction field Bz, causes K , the integral of motion constant, to be important. The difference CA - K) is similar to what we called the generalised AB effect, though in the present case the motion is aperiodic. 5. Problems with, and Criticisms of, Experiments and the AB Effect Itself We discuss the structure of various experiments, and also experimental topics that are closely related to theory.

Critics often appear to have forgotten this basic property. In Refs. 23] authors have used "inaccessible field" or similar arguments in order to deny that the AB effect can occur. 26].

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