Separation of quantum time evolution into holonomic and dynamical parts

Abstract

The issue of separating Schrödinger-type quantum time evolution into a product of holonomic and dynamical parts in the non-adiabatic non-Abelian case is examined. We identify all special cases in which this kind of separation is possible, and we prove that separability is a gauge invariant property of quantum time evolution. The general analysis is implemented in a three-level system with $\hat{I}›$-type coupling structures. The typical case where the holonomic and dynamical parts do not separate is illustrated by means of two non-commuting $\hat{I}›$-type Hamiltonians.

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• Comment on "Evolution Operator Can Always Be Separated into the Product of Holonomy and Dynamic Operators"