Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate

Area of Science:

• Quantum physics
• Fluid dynamics
• Condensed matter physics

Background:

• Two-component Bose-Einstein condensates (BECs) exhibit complex dynamics from discontinuous initial profiles.
• The system's dynamics can be simplified to a single polarization mode, analogous to magnetic excitations in ferromagnets.

Purpose of the Study:

• To classify possible flows of two-component BECs.
• To analyze the dynamics governed by an equation equivalent to the Landau-Lifshitz equation.
• To investigate the implications of non-genuine nonlinearity on wave patterns.

Main Methods:

• Derivation of one-phase periodic solutions for the BEC system.
• Obtaining Whitham modulation equations and their connection to Riemann invariants.
• Comparison of analytical results with numerical simulations.

Main Results:

• Full set of one-phase periodic solutions presented.
• Non-single-valued mapping between Whitham equation solutions and physical wave patterns observed.
• Identification of contact dispersive shock waves, absent in genuinely nonlinear systems.

Conclusions:

• The non-genuine nonlinearity of the system leads to unique wave phenomena.
• Analytic findings are robustly confirmed by numerical simulations.
• This work provides a comprehensive classification of BEC flows and highlights novel dispersive shock wave behavior.