Nonadiabatic geometric angle in nuclear magnetic resonance connection. (English) Zbl 1077.81514

Cherbal, Omar; Maamache, Mustapha; Drir, Mahrez

Mladenov, Ivaïlo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3–10, 2004. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-9-5/pbk). 175-182 (2005).

Summary: By using the Grassmannian invariant-angle coherents states approach, the classical analogue of the Aharonov-Anandan nonadiabatic geometrical phase is found for a spin one-half in Nuclear Magnetic Resonance (NMR). In the adiabatic limit, the semi-classical relation between the adiabatic Berry’s phase and Hannay’s angle gives exactly the experimental result observed by D. Suter et al. [Mol. Phys. 61, 1327–1340 (1987)].
For the entire collection see [Zbl 1066.53003].

MSC:

81Q70

Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory