2008/07/23 by N A Sinitsyn, N. A. Sinitsyn, Avadh Saxena · 8 citations
Mathematics · Physics and Astronomy · #Frenet–Serret formulas #Geometric phase #Geometric shape #Hamiltonian (control theory) #Hamiltonian system #Interpretation (philosophy) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Stochastic process #Unit circle #Unit vector #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/41/39/392002
published in Journal of Physics A Mathematical and Theoretical 41(39), 392002 (Institute of Physics) · 10 pages 2 figures
arxiv created 2008/07/23 · openalex publication_date 2008/09/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.