Jain Mudit, Amin Mustafa A, Pu Han
Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA.
Phys Rev E. 2023 Nov;108(5-2):055305. doi: 10.1103/PhysRevE.108.055305.
We provide an algorithm, i-SPin 2, for evolving general spin-s Gross-Pitaevskii or nonlinear Schrödinger systems carrying a variety of interactions, where the 2s+1 components of the "spinor" field represent the different spin-multiplicity states. We consider many nonrelativistic interactions up to quartic order in the Schrödinger field (both short and long range, and spin-dependent and spin-independent interactions), including explicit spin-orbit couplings. The algorithm allows for spatially varying external and/or self-generated vector potentials that couple to the spin density of the field. Our work can be used for scenarios ranging from laboratory systems such as spinor Bose-Einstein condensates (BECs), to cosmological or astrophysical systems such as self-interacting bosonic dark matter. As examples, we provide results for two different setups of spin-1 BECs that employ a varying magnetic field and spin-orbit coupling, respectively, and also collisions of spin-1 solitons in dark matter. Our symplectic algorithm is second-order accurate in time, and is extensible to the known higher-order-accurate methods.
我们提供了一种名为i-SPin 2的算法，用于演化具有各种相互作用的一般自旋-s 格罗斯-皮塔耶夫斯基或非线性薛定谔系统，其中“自旋张量”场的2s + 1个分量代表不同的自旋多重态状态。我们考虑了薛定谔场中高达四次方阶的许多非相对论相互作用（包括短程和长程、自旋相关和自旋无关的相互作用），包括显式的自旋-轨道耦合。该算法允许存在与场的自旋密度耦合的空间变化的外部和/或自生矢量势。我们的工作可用于从实验室系统（如自旋玻色-爱因斯坦凝聚体（BEC））到宇宙学或天体物理系统（如自相互作用玻色子暗物质）等各种场景。作为示例，我们给出了两种不同设置的自旋-1 BEC的结果，它们分别采用了变化的磁场和自旋-轨道耦合，以及暗物质中自旋-1孤子的碰撞。我们的辛算法在时间上具有二阶精度，并且可以扩展到已知的高阶精度方法。
