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理论物理通讯：英文版

Computing Ground State Solution of Bose-Einstein Condensates Trapped in One-Dimensional Harmonic Potential

Yuan, Qingxin, Ding Ding, Guohui

Published Jan 1, 2006• 1 citation
OpenAlex

Abstract

为在一个泛音潜力套住很好的 Bose 爱因斯坦冷凝物，我们从解决时间依赖者的现在的数字结果非线性的 Schroedinger 方程基于的在 Crank-Nicolson 方法。与这个方法，我们能由发展试用发现扎根的州的波浪功能和精力在真实、想象的时间空格的起始的波浪功能分别地。在实时空间，结果与一致[Phys。加快。一 51 (1995 ) 4704 ] ，但是试用波浪功能在一个很小的范围被限制。在想象的时间空间，相反，试用波浪函数能广泛地被选择，而且，结果是稳定的。

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为在一个泛音潜力套住很好的 Bose 爱因斯坦冷凝物，我们从解决时间依赖者的现在的数字结果非线性的 Schroedinger 方程基于的在 Crank-Nicolson 方法。与这个方法，我们能由发展试用发现扎根的州的波浪功能和精力在真实、想象的时间空格的起始的波浪功能分别地。在实时空间，结果与一致[Phys。加快。一 51 (1995 ) 4704 ] ，但是试用波浪功能在一个很小的范围被限制。在想象的时间空间，相反，试用波浪函数能广泛地被选择，而且，结果是稳定的。
For Bose–Einstein condensates trapped in a harmonic potential well, we present numerical results from solving the time-dependent nonlinear Schrodinger equation based on the Crank–Nicolson method. With this method we are able to find the ground state wave function and energy by evolving the trial initial wave function in real and imaginary time spaces, respectively. In real time space, the results are in agreement with [Phys. Rev. A 51 (1995) 4704], but the trial wave function is restricted in a very small range. On the contrary, in imaginary time space, the trial wave function can be chosen widely, moreover, the results are stable.
我们与我们由迪拉克功能为酒窝潜力建模的一个酒窝潜力在一个线性陷井学习 BoseEinstein 冷凝作用。吸引人、排斥的酒窝潜力被考虑。这个模型允许 noninteracting 气体的简单、明确的数字、分析的调查。因此， Schr ? dinger 方程被使用而不是 GrossPitaevski 方程。我们计算原子密度，化学潜力，批评温度和冷凝物部分。关于在在提高的温度的大冷凝物形成的线性陷井的酒窝潜力的相对深度的角色清楚地被揭示。而且，我们也为象熵经分解那样的精明的各种各样的数量介绍一个半古典作品方法。而且，我们把这份报纸的结果与有在 1D 的一个酒窝潜力的泛音陷井在被调查的一份以前的报纸的结果作比较。
We develop time-splitting finite-difference methods, using an implicit Backward–Euler and a semi-implicit Crank–Nicolson discretization schemes, to study the spin-orbit-coupled (SO-coupled) spinor Bose–Einstein condensates with coherent coupling in quasi-one- and quasi-two-dimensional traps. The split equations involving kinetic energy and spin-orbit-coupling operators are solved using either a time implicit Backward–Euler or a semi-implicit Crank–Nicolson method. We explicitly develop the methods for pseudospin-1/2, spin-1 and spin-2 condensates. The results for ground states obtained with time-splitting Backward–Euler and Crank–Nicolson methods are in excellent agreement with time-splitting Fourier spectral method, which is one of the popular methods to solve the mean-field models for SO-coupled spinor condensates. We confirm the emergence of different phases in SO-coupled pseudospin-1/2, spin-1 and spin-2 condensates with coherent coupling.
We develop time-splitting finite-difference methods, using an implicit Backward–Euler and a semi-implicit Crank–Nicolson discretization schemes, to study the spin-orbit-coupled (SO-coupled) spinor Bose–Einstein condensates with coherent coupling in quasi-one- and quasi-two-dimensional traps. The split equations involving kinetic energy and spin-orbit-coupling operators are solved using either a time implicit Backward–Euler or a semi-implicit Crank–Nicolson method. We explicitly develop the methods for pseudospin-1/2, spin-1 and spin-2 condensates. The results for ground states obtained with time-splitting Backward–Euler and Crank–Nicolson methods are in excellent agreement with time-splitting Fourier spectral method, which is one of the popular methods to solve the mean-field models for SO-coupled spinor condensates. We confirm the emergence of different phases in SO-coupled pseudospin-1/2, spin-1 and spin-2 condensates with coherent coupling.