Geometry of quantum active subspaces and of effective Hamiltonians
David Viennot · Journal of Mathematical Physics · 2007
We propose a geometric formulation of the theory of effective Hamiltonians associated with active spaces. We analyze particularly the case of the time-dependent wave operator theory. This formulation is related to the geometry of the manifold of the active spaces, particularly to its Kählerian structure. We introduce the concept of quantum distance between active spaces. We show that the time-dependent wave operator theory is, in fact, a gauge theory, and we analyze its relationship with the geometric phase concept.