Improvement in complex Langevin dynamics from a view point of Lefschetz thimbles
Improvement in complex Langevin dynamics from a view point of Lefschetz thimbles
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从 Lefschetz 顶针的角度来看复杂 Langevin 动力学的改进
DOI：
10.1103/physrevd.94.074009
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发表时间：
2016
影响因子：
5
通讯作者：
Takahiro M. Doi
中科院分区：
文献类型：
--
作者：
Shoichiro Tsutsui;Takahiro M. Doi
我们开发了一种方法来改善复杂的Langevin动力学的莱夫谢茨-顶针分解的积分的动机。在我们的方法中，任意可观的原始模型与多Lefschetz顶针计算修改后的模型与一个单一的顶针。我们将我们的修改方法应用于一维积分，其中复杂的Langevin动力学的天真实现由于严重的符号问题而无法再现精确的结果。我们表明，玩具模型可以修改，使新的模型包括一个单一的莱夫谢茨顶针。我们发现，改进的复朗之万动力学可以得到正确的结果。
We develop a way of improving complex Langevin dynamics motivated by the Lefschetz-thimble decomposition of integrals. In our method, arbitrary observables of an original model with multiple Lefschetz thimbles are computed by a modified model with a single thimble. We apply our modification method to a one-dimensional integral in which the naive implementation of the complex Langevin dynamics fails to reproduce the exact results due to the severe sign problem. We show that the toy model can be modified so that the new model consists of a single Lefschetz thimble. We find that correct results can be obtained by the improved complex Langevin dynamics.