Hannay angles and Grassmannian action-angle quantum states
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 278-289
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We show how to derive the Hannay angles of Grassmannian classical mechanics from the evolution of Grassmannian action–angle quantum states. Just as in the commutative case, this evolution defines a geometric transport, which can also be obtained from a quantum canonical transformation or a variational principle. As examples, we explicitly construct the quantum states for the classical counterparts of a first- and second-quantized $N$-level system. In the latter case, these states reduce to standard fermionic coherent states and the classical Hannay angles coincide with the quantum Berry phases.
Keywords:
Berry phase, Hannay angle, action–angle fermionic coherent state.
@article{TMF_2020_202_2_a6,
author = {H. Lakehal and M. Maamache},
title = {Hannay angles and {Grassmannian} action-angle quantum states},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {278--289},
publisher = {mathdoc},
volume = {202},
number = {2},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a6/}
}
H. Lakehal; M. Maamache. Hannay angles and Grassmannian action-angle quantum states. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 278-289. http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a6/