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arXiv 1503.05088hep-lat
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具有低阶耦合的格点系统的有效数值解

On the efficient numerical solution of lattice systems with low-order couplings

A. Ammon, A. Genz, T. Hartung, K. Jansen, H. Leövey, J. Volmer

摘要:

我们应用拟蒙特卡罗(QMC)和递归数值积分方法计算了量子力学非谐振子和拓扑量子力学转子模型的欧几里得离散时间路径积分。对于非谐振子,这两种方法都优于标准的马尔可夫链蒙特卡罗方法,并显示出显着改善的误差缩放。然而,对于量子力学转子,我们不能找到一个成功的方法,采用QMC。另一方面,递归数值积分方法对该模型非常有效,并且显示出至少指数级的快速误差缩放。

英文摘要:

We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model. For the anharmonic oscillator both methods outperform standard Markov Chain Monte Carlo methods and show a significantly improved error scaling. For the quantum mechanical rotor we could, however, not find a successful way employing QMC. On the other hand, the recursive numerical integration method works extremely well for this model and shows an at least exponentially fast error scaling.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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