By James Hamilton
The Aharonov-Bohm impression is linked to cyclic movement. it's one among a few anholonomic results, and which means the dynamical description will depend on the present place of the approach 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 influence - a gentle beam passing round a circled procedure of mirrors - is one other instance. sleek dynamical advancements corresponding to Hannay's perspective and Berry's part are additional helpful examples.
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Extra resources for Aharonov-Bohm and other Cyclic Phenomena
3) will he ignored. 17). 18b) 28 3. Generalization of the Aharonov-Bohm Effect Energy A2 Fig. 1. 8a). 6). 1) does not alter the energy, so r would be the solution of Schr6dinger's equation, Eq. 4a), for an electron confined by a potential Vc(0) alone, so that it moves on the circle p = P0 with angular momentum A. 18a) is a generalization of the AB relation. We call ~o(x) the '~eld-free" wave function. In Fig. 1 the confining potential and the centrifugal potential are shown. X0(P), the radial component of ~0, will be negligible except in a small segment around the minimum of A2 + yelp) 9 The minimum is to be at Po.
3) is useful because the induction field B is such that A can be of the form (0,O,As(p)) (in cylindrical coordinates). Thus B is restricted to the form (Bz(p), O,0). (iv) Ginsburg-Landau Theory. 5]. 9). 11) 26 3. Generalization of the Aharonov-Bohm Effect The parameters Fn, a, ~ may depend on the temperature, and in the GL theory m (in the last term) is taken to be the mass of the electron, although r is the wave function of the Cooper pair. Here Ir can be normalised as ns, the superconducting electron density.
4a) is used. 9d) shows that we require M to be fairly large in order to give a well-defined orbit even when the lowest value, n = 0, is used. 9d) is to be multiplied by (2n + 1) 1/2 for n > 0. 17) The integration has been taken along the path of the wave packet, starting at 0 = 0. 2b). 35, 35a). 3) will he ignored. 17). 18b) 28 3. Generalization of the Aharonov-Bohm Effect Energy A2 Fig. 1. 8a). 6). 1) does not alter the energy, so r would be the solution of Schr6dinger's equation, Eq. 4a), for an electron confined by a potential Vc(0) alone, so that it moves on the circle p = P0 with angular momentum A.
Aharonov-Bohm and other Cyclic Phenomena by James Hamilton