Linear dynamical systems, coherent state manifolds, flows, and matrix Riccati equation

Abstract

The classical motion and the quantum evolution determined by linear Hamiltonians on coherent state manifolds of compact and noncompact Hermitian symmetric space structure are considered. A matrix Riccati equation, with opposite signs of the quadratic terms in the compact and noncompact cases, determines the classical motion and the quantum evolution. The geometric meaning of equations of motion as flow on a complex Grassmann manifold and his noncompact dual is emphasized. Possibilities of generalizing the results to flag manifolds are pointed out.