Canonical form of the Evolution Operator of a Time-Dependent Hamiltonian in the Three Level System

Abstract

In this paper we study the evolution operator of a time-dependent Hamiltonian in the three level system. The evolution operator is based on $SU(3)$ and its dimension is $8$, so we obtain three complex Riccati differential equations interacting with one another (which have been obtained by Fujii and Oike) and two real phase equations. This is a canonical form of the evolution operator.

Latex 10 pages; no figure

References in corpus (2)

• Riccati Diagonalization of Hermitian Matrices
• A Geometric Parametrization of the Cabibbo-Kobayashi-Maskawa Matrix and the Jarlskog Invariant