Classical periodic orbits in extended phase space for spherical harmonic oscillator with spin-orbit coupling

Area of Science:

• Quantum Mechanics
• Classical Mechanics
• Atomic Physics

Background:

• Spherical harmonic oscillators are fundamental systems in physics.
• Spin-orbit coupling significantly influences atomic and molecular systems.
• Understanding periodic orbits (POs) is crucial for analyzing dynamical systems.

Purpose of the Study:

• To conduct a comprehensive analysis of classical periodic orbits (POs) and their bifurcations.
• To investigate the role of spin-orbit coupling in a spherical harmonic oscillator system.
• To explore the interplay between orbital motion and spin precession.

Main Methods:

• Explicit consideration of spin motion using spin canonical variables.
• Application of semiclassical approximation to spin coherent state path-integral representation.
• Analytical derivation of generic expressions for identified periodic orbits.

Main Results:

• Identified diametric and two circular PO families with frozen spin.
• Discovered novel solutions bridging circular POs, exhibiting coupled orbital-spin motion.
• Found secondary bifurcations on these bridging solutions, creating new, stable POs at higher energies.

Conclusions:

• The study provides a full analytical description of peculiar bifurcation scenarios in the system.
• New insights into the complex dynamics of systems with spin-orbit coupling have been revealed.
• The findings contribute to a deeper understanding of classical periodic orbits in quantum-influenced systems.