Abstract Here, we present simple and efficient numerical scheme to study static and dynamic properties of spin-1 Bose–Einstein condensates (BECs) with spin–orbit (SO) coupling by solving three coupled Gross–Pitaevskii equations (CGPEs) in three-, quasi-two and quasi-one dimensional systems. We provide a set of three codes developed in FORTRAN 90/95 programming language with user defined ‘option’ of imaginary and real-time propagation. We present the numerical results for energy, chemical potentials, and component densities for the ground state and compare with the available results from the literature. The results are presented for both the ferromagnetic and antiferromagnetic spin-1 BECs with and without SO coupling. To improve the computational speed, all the codes have the option of OpenMP parallelization. We have also presented the results for speedup and efficiency of OpenMP parallelization for the three codes with both imaginary and real-time propagation. Program summary Program Title: FORTRESS CPC Library link to program files: http://dx.doi.org/10.17632/st7md3ss85.1 Licensing provisions: MIT Programming language: (OpenMP) FORTRAN 90/95 External routines/libraries: FFTW 3.3.8 Nature of problem: To solve the coupled Gross–Pitaevskii equations for spin-1 BEC with anisotropic spin–orbit coupling using the time-splitting spectral method. Solution method: We use the time-splitting Fourier spectral method to solve the coupled Gross–Pitaevskii equations. The resulting equations are evolved in imaginary time to obtain the ground state of the system or in real-time to study the dynamics.

中文翻译：

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FORTRESS：用于求解自旋-轨道耦合自旋 1 玻色-爱因斯坦凝聚的耦合 Gross-Pitaevskii 方程的 FORTRAN 程序

摘要 在这里，我们提出了简单有效的数值方案，通过求解三个耦合的 Gross-Pitaevskii 方程 (CGPEs) 来研究具有自旋轨道 (SO) 耦合的自旋 1 玻色-爱因斯坦凝聚体 (BECs) 的静态和动态特性，准二维和准一维系统。我们提供了一组用 FORTRAN 90/95 编程语言开发的三个代码，带有用户定义的虚拟和实时传播“选项”。我们提供了基态的能量、化学势和成分密度的数值结果，并与文献中的可用结果进行了比较。结果显示了具有和不具有 SO 耦合的铁磁和反铁磁自旋 1 BEC。为了提高计算速度，所有代码都提供了 OpenMP 并行化选项。我们还展示了三种具有虚数和实时传播的代码的 OpenMP 并行化的加速和效率结果。程序概要 程序名称：FORTRESS CPC 库程序文件链接：http://dx.doi.org/10.17632/st7md3ss85.1 许可条款：MIT 编程语言：(OpenMP) FORTRAN 90/95 外部例程/库：FFTW 3.3。 8 问题性质：使用时分谱法求解具有各向异性自旋轨道耦合的自旋 1 BEC 的耦合 Gross-Pitaevskii 方程。求解方法：我们使用分时傅立叶谱法来求解耦合的 Gross-Pitaevskii 方程。由此产生的方程在虚时间演化以获得系统的基态或实时演化以研究动力学。