Phase Splitting for Periodic Lie Systems

Abstract

In the context of the Floquet theory, using a variation of parameter argument, we show that the logarithm of the monodromy of a real periodic Lie system with appropriate properties admits a splitting into two parts, called dynamic and geometric phases. The dynamic phase is intrinsic and linked to the Hamiltonian of a periodic linear Euler system on the co-algebra. The geometric phase is represented as a surface integral of the symplectic form of a co-adjoint orbit.

(v1) 15 pages. (v2) 16 pages. Some typos corrected. References and further comments added. Final version to appear in J. Phys. A.

References in corpus (4)

• Superposition rules, Lie theorem and partial differential equations
• Integrability of Lie systems and some of its applications in physics
• A geometric approach to time evolution operators of Lie quantum systems
• Quantum Lie systems and integrability conditions

Cited by in corpus (6)

• From constants of motion to superposition rules for Lie-Hamilton systems
• Dirac--Lie systems and Schwarzian equations
• Lie--Hamilton systems: theory and applications
• Mixed superposition rules and the Riccati hierarchy
• On Lie systems and Kummer-Schwarz equations
• Quantum quasi-Lie systems: properties and applications