Solitons in Inhomogeneous Gauge Potentials: Integrable and Nonintegrable Dynamics

Area of Science:

• Nonlinear physics
• Quantum mechanics
• Condensed matter physics

Background:

• Spinor solitons are complex quantum phenomena.
• Integrable models simplify the study of nonlinear dynamics.
• Bose-Einstein condensates offer a platform for studying quantum systems.

Purpose of the Study:

• Introduce an exactly integrable nonlinear model for spinor soliton dynamics.
• Investigate the influence of space-dependent matrix gauge potentials.
• Analyze the crossover between integrable and nonintegrable regimes.

Main Methods:

• Developed an exactly integrable nonlinear model.
• Established gauge equivalence to the Manakov model (vector nonlinear Schrödinger equations).
• Studied a Bose-Einstein condensate with random spin-orbit coupling and Zeeman splitting.

Main Results:

• The model is gauge equivalent to the Manakov model.
• In a disordered spin-orbit coupling landscape, zero Zeeman splitting leads to non-scattering soliton motion.
• Nonzero Zeeman splitting causes soliton scattering, but integrability is restored at large splitting.

Conclusions:

• Zeeman splitting acts as a control parameter for the crossover between integrable limits in spinor soliton dynamics.
• The developed model provides a framework for understanding soliton behavior in complex potentials.
• This research offers insights into quantum dynamics in disordered systems.