Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve
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 77, 58001 (2007)], and use it to derive the stochastic system response to periodic parameter variations.
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