Integrator for general spin-s Gross-Pitaevskii systems

Area of Science:

• Quantum physics
• Computational physics

Background:

• Spinor fields in quantum systems are described by Gross-Pitaevskii or nonlinear Schrödinger equations.
• Simulating these systems requires robust numerical methods to handle complex interactions.

Purpose of the Study:

• To introduce i-SPin 2, a novel algorithm for evolving general spin-s Gross-Pitaevskii and nonlinear Schrödinger systems.
• To incorporate a wide range of nonrelativistic interactions, including spin-dependent and spin-orbit couplings.
• To enable simulations with spatially varying vector potentials affecting spin density.

Main Methods:

• Development of the i-SPin 2 algorithm, a second-order accurate symplectic method.
• Inclusion of nonrelativistic interactions up to quartic order (short and long range).
• Accommodation of explicit spin-orbit couplings and spatially varying potentials.

Main Results:

• Demonstration of the algorithm's capability to simulate diverse spin systems.
• Presentation of results for spin-1 Bose-Einstein condensates with varying magnetic fields and spin-orbit coupling.
• Simulation of spin-1 soliton collisions in dark matter scenarios.

Conclusions:

• The i-SPin 2 algorithm provides a versatile tool for simulating complex spinor quantum systems.
• The method is applicable to both laboratory experiments (e.g., BECs) and astrophysical phenomena (e.g., dark matter).
• The algorithm is extensible to higher-order accurate methods for advanced simulations.