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arXiv · 0807.3121

Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve

N. A. Sinitsyn·Avadh Saxena
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Abstract

We develop a new interpretation of the geometric phase in evolution with a non-Hermitian real value 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 in [N. A. Sinitsyn and I. Nemenman, EPL {\bf 77}, 58001 (2007)], and use it to derive the stochastic system response to periodic parameter variations.

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N. A. Sinitsyn, Avadh Saxena. 2008-07-23. Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve. https://doi.org/10.1088/1751-8113/41/39/392002

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