N A Sinitsyn and Avadh Saxena 2008 J. Phys. A: Math. Theor. 41 392002 doi:10.1088/1751-8113/41/39/392002
Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve
FREE ARTICLEN A Sinitsyn1 and Avadh Saxena2
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We develop an interpretation of the geometric phase in evolution with a non-Hermitian real-valued Hamiltonian by relating it to the angle developed during the parallel transport along a closed curve by a unit vector triad in the 3D Minkovsky space. We also show that this geometric phase is responsible for the anholonomy effects in stochastic processes considered by Sinitsyn and Nemenman (2007 Europhys. Lett. 77 58001), and use it to derive the stochastic system response to periodic parameter variations.
- PACS
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03.65.Vf Phases: geometric; dynamic or topological
03.65.Ta Foundations of quantum mechanics; measurement theory
- MSC
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81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
81P20 Stochastic mechanics (including stochastic electrodynamics)
- Subjects
- Dates
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Issue 39 (3 October 2008)
Received 20 June 2008
Published 2 September 2008
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Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve
N A Sinitsyn and Avadh Saxena 2008 J. Phys. A: Math. Theor. 41 392002
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