N A Sinitsyn and J Ohkubo 2008 J. Phys. A: Math. Theor. 41 262002 doi:10.1088/1751-8113/41/26/262002
Hannay angle and geometric phase shifts under adiabatic parameter changes in classical dissipative systems
FREE ARTICLEN A Sinitsyn1 and J Ohkubo2
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Kepler and Kagan (1991 Phys. Rev. Lett. 66 847) derived a geometric phase shift in dissipative limit cycle evolution. This effect was considered as an extension of the geometric phase in classical mechanics. We show that the opposite is also true, namely, this geometric phase can be identified with the classical mechanical Hannay angle in an extended phase space. Our results suggest that this phase can be generalized to a stochastic evolution with an additional noise term in evolution equations.
- PACS
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03.65.Ta Foundations of quantum mechanics; measurement theory
- MSC
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81P20 Stochastic mechanics (including stochastic electrodynamics)
81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
- Subjects
- Dates
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Issue 26 (11 July 2008)
Received 19 April 2008
Published 4 June 2008
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Hannay angle and geometric phase shifts under adiabatic parameter changes in classical dissipative systems
N A Sinitsyn and J Ohkubo 2008 J. Phys. A: Math. Theor. 41 262002
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