Ray space Riccati evolution and geometric phases for N-level quantum systems
Quantum Physics
2008-11-26 v1
Abstract
We present a simple derivation of the matrix Riccati equations governing the reduced dynamics as one descends from the group U(N) describing the Schroedinger evolution of an N-level quantum system to the various coset spaces, Grassmanian manifolds, associated with it. The special case pertaining to the geometric phase in N-level systems is described in detail. Further, we show how the matrix Riccati equation thus obtained can be reformulated as an equation describing Hamiltonian evolution in a classical phase space and establish correspondences between the two descriptions.
Keywords
Cite
@article{arxiv.0706.0964,
title = {Ray space Riccati evolution and geometric phases for N-level quantum systems},
author = {S. Chaturvedi and E. Ercolessi and G. Marmo and G. Morandi and N. Mukunda and R. Simon},
journal= {arXiv preprint arXiv:0706.0964},
year = {2008}
}