Rooney S J, Blakie P B, Bradley A S
Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin, New Zealand.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):013302. doi: 10.1103/PhysRevE.89.013302. Epub 2014 Jan 10.
We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional weakly interacting Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes in the low-energy classical region of the system, and evaluating terms from the number-conserving scattering reservoir process. We give an accurate and efficient procedure for evaluating the scattering terms using a Hermite-polynomial based spectral-Galerkin representation, which allows us to precisely implement the low-energy mode restriction. Stochastic integration is performed using the weak semi-implicit Euler method. We extensively characterize the accuracy of our method, finding a faster-than-expected rate of stochastic convergence. Physical consistency of the algorithm is demonstrated by considering thermalization of initially random states.
我们提出了一种用于求解在谐振子捕获势中三维弱相互作用玻色气体的随机投影格罗斯 - 皮塔耶夫斯基方程（SPGPE）的方法。SPGPE面临的挑战包括在系统的低能经典区域精确演化所有模式，以及评估来自数守恒散射库过程的项。我们给出了一种基于埃尔米特多项式的谱伽辽金表示来评估散射项的精确且高效的程序，这使我们能够精确地实现低能模式限制。随机积分使用弱半隐式欧拉方法进行。我们广泛地刻画了我们方法的精度，发现其随机收敛速度比预期的要快。通过考虑初始随机态的热化来证明算法的物理一致性。
