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

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

2008-07-19

arxiv.org/abs/0807.3121v2

J. Phys. A: Math. Theor. 41 (2008) 392002

Physics

Condensed Matter

Statistical Mechanics

10 pages 2 figures

Scientific paper

10.1088/1751-8113/41/39/392002

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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