Geometric Phases for Three State Systems

Abstract

The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would appear in a three dimensional quantum system with adiabatic characteristics are given explicitly. This is done in terms of the Euler angle parameterization of SU(3) which enables a straight-forward calculation of these quantities and its immediate generalization.

13 pages, LaTeX2e

References in corpus (4)

• The Quantum Adiabatic Approximation and the Geometric Phase
• SU(3) Revisited
• Density Matrices and Geometric Phases for n-state Systems
• Non-Abelian Geometrical Phase for General Three-Dimensional Quantum Systems

Cited by in corpus (5)

• Generalized Euler Angle Paramterization for SU(N)
• Generalized Euler Angle Parameterization for U(N) with Applications to SU(N) Coset Volume Measures
• Geometric and Majorana phases in neutrino oscillations
• On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices
• Twisted CP(N-1) instanton projectors and the N-level quantum density matrix