Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method
Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method
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类似于复朗之万法的 Lefschetz-顶针积分的 Hamilton 动力学
DOI：
10.1093/ptep/ptv152
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发表时间：
2015
影响因子：
3.5
通讯作者：
Yuya Tanizaki
中科院分区：
文献类型：
--
作者：
Kenji Fukushima;Yuya Tanizaki
lefschetz -顶针法，即沿最陡下降环积分，是一种通过使理论复杂化来避免符号问题的方法。我们讨论了这种最陡的下降周期可以被识别为超对称汉密尔顿动力学的基态波函数，这是用类似于复朗之万方法的框架来描述的。我们用一个玩具模型在网格上数值构造了波函数，并证实了它们的良好定域行为。
The Lefschetz-thimble method, i.e., integration along the steepest descent cycles, is a way to avoid the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state wave functions of a supersymmetric Hamilton dynamics, which is described with a framework akin to the complex Langevin method. We numerically construct the wave functions on a grid using a toy model and confirm their well-localized behavior.