dorsal/arxiv
View SchemaAdiabatic Berry Phase and Hannay Angle for Open Paths
| Authors | Arun Kumar Pati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9804057 |
| URL | https://arxiv.org/abs/quant-ph/9804057 |
| DOI | 10.1006/aphy.1998.5850 |
| Journal | Annals Phys.270:178-197,1998 |
Abstract
We obtain the adiabatic Berry phase by defining a generalised gauge potential whose line integral gives the phase holonomy for arbitrary evolutions of parameters. Keeping in mind that for classical integrable systems it is hardly clear how to obtain open-path Hannay angle, we establish a connection between the open-path Berry phase and Hannay angle by using the parametrised coherent state approach. Using the semiclassical wavefunction we analyse the open-path Berry phase and obtain the open-path Hannay angle. Further, by expressing the adiabatic Berry phase in terms of the commutator of instantaneous projectors with its differential and using Wigner representation of operators we obtain the Poisson bracket between distribution function and its differential. This enables us to talk about the classical limit of the phase holonomy which yields the angle holonomy for open-paths. An operational definition of Hannay angle is provided based on the idea of classical limit of quantum mechanical inner product. A probable application of the open-path Berry phase and Hannay angle to wave-packet revival phenomena is also pointed out.
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"abstract": "We obtain the adiabatic Berry phase by defining a generalised gauge potential\nwhose line integral gives the phase holonomy for arbitrary evolutions of\nparameters. Keeping in mind that for classical integrable systems it is hardly\nclear how to obtain open-path Hannay angle, we establish a connection between\nthe open-path Berry phase and Hannay angle by using the parametrised coherent\nstate approach. Using the semiclassical wavefunction we analyse the open-path\nBerry phase and obtain the open-path Hannay angle. Further, by expressing the\nadiabatic Berry phase in terms of the commutator of instantaneous projectors\nwith its differential and using Wigner representation of operators we obtain\nthe Poisson bracket between distribution function and its differential. This\nenables us to talk about the classical limit of the phase holonomy which yields\nthe angle holonomy for open-paths. An operational definition of Hannay angle is\nprovided based on the idea of classical limit of quantum mechanical inner\nproduct. A probable application of the open-path Berry phase and Hannay angle\nto wave-packet revival phenomena is also pointed out.",
"arxiv_id": "quant-ph/9804057",
"authors": [
"Arun Kumar Pati"
],
"categories": [
"quant-ph"
],
"doi": "10.1006/aphy.1998.5850",
"journal_ref": "Annals Phys.270:178-197,1998",
"title": "Adiabatic Berry Phase and Hannay Angle for Open Paths",
"url": "https://arxiv.org/abs/quant-ph/9804057"
},
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