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

N A Sinitsyn, Avadh Saxena
2008 Journal of Physics A: Mathematical and Theoretical  
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
more » ... nse to periodic parameter variations.
doi:10.1088/1751-8113/41/39/392002 fatcat:3clsie2yg5cnrlypbvwdxdbblq