By James Hamilton

The Aharonov-Bohm impression is linked to cyclic movement. it truly is considered one of a couple of anholonomic results, and which means the dynamical description is dependent upon the present place of the method 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 gentle beam passing round a circled process of mirrors - is one other instance. smooth dynamical advancements akin to Hannay's attitude and Berry's section are additional helpful examples.

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11) can be ignored. 13) for the behaviour of r in the presence of the magnetic field. 13) with the analogous solutions for the electron at the start of Sect. 9c) that the least value of ((P --/90)2) occurs for n = 0. 13). 13a) where wc = 2WB. 9c) also shows that a non-zero value of f ( T ) implies that the field H cannot exceed a maximum value. In this model that is the critical field Hc2. 14) (where q = 2e). 15) -- 2q#0Hc2 This agrees with the idea of the parameter I(T) as expressed above. (See for example, Chap.

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. Other topics are included that have a bearing on some of the numerous discussions on the existence of the AB effect and its nature. , that are in the literature. 2] and elsewhere. Biprism electron interference experiments, and the limitations on such measurements, are discussed, together with the problem of distinguishing the fringe shift from the profile shift.

The adiabatic principle (as shown in Sect. 3) does not give a simple prescription for how slow any variation of the parameters has to be in order to be adiabatic. A degeneracy in several frequencies, occurring as a parameter a(t) varies, can invalidate the result; as can the situation in which a frequency w goes to zero. Several proofs of the adiabatic theorem, stating various other exceptions and conditions, appear in standard texts, e. g. E. 1], V. I. 2]. 20). B is the induction on the standard circle p -- pT.