By James Hamilton
The Aharonov-Bohm impact is linked to cyclic movement. it's considered one of a few anholonomic results, and which means the dynamical description will depend on the present place of the procedure and at the direction through 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 circled procedure of mirrors - is one other instance. smooth dynamical advancements equivalent to Hannay's attitude and Berry's section are additional worthwhile examples.
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Additional info for Aharonov-Bohm and other Cyclic Phenomena
6a). We use the symbol/170 to denote a spread such that there is a 70 % chance (in the Gaussian case) of the event lying within it [cf. 3) below]. 8) with the equality holding for a Ganssian minimum uncertainty profile. We arbitrarily choose the condition: 1 6 A~opz < -~( Pz)2~ , with d~ (Spz)2~ = e ~ z This should ensure the validity of Pryce's argument. 7a) is to be valid. This result can be understood in another fashion. Scanning along a line y = const, in Fig. 5, fringes appear at separation (co/bo)[zf I, and that is equivalent to separation Izf[ on x = - f .
9]. The equivalent electron optics description with rectilinear propagation and mutually coherent sources $1,$2 is shown in Fig. 2. When B = 0 in the solenoid, the intensity observed at Q is where ~i, r are the wave packets (of mean wavelength ~) passing via DI, D2 respectively. 1) 46 5. Problems with, and Criticisms of, Experiments and the AB Effect Itself ~--- a 0 --~ ~176 -'- 'i\' O. x~, :\I V>y Q ) 0 Q Fig. 1. Biprism electron interferences (angles exaggerated) ~176 v ~Y Fig. 2. 1a) It can be seen from Fig.
The material presented in the present article will lead to the following scenario. The AB phase arising from the cylindrical solenoid discussed in 54 5. Problems with, and Criticisms of, Experiments and the AB Effect Itseff Chap. 3); there appears to be no other simple derivation. However, if the flux 4~ in the solenoid is slowly altered in time, electromagnetic induction, as in Sect. 7, gives the new AB phase. Similarly if the solenoid is no longer cylindrical but is finely tapered then Pryce's effect gives the AB phase.