Complex Langevin: etiology and diagnostics of its main problem
Complex Langevin: etiology and diagnostics of its main problem
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DOI：
10.1140/epjc/s10052-011-1756-5
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发表时间：
2011-01
期刊：
影响因子：
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通讯作者：
G. Aarts;Frank A. J. L. James;E. Seiler;I. Stamatescu
中科院分区：
文献类型：
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作者：
G. Aarts;Frank A. J. L. James;E. Seiler;I. Stamatescu
复朗之万方法是解决各种物理情况下出现的所谓符号问题的主要候选者。它最令人烦恼的问题是，有时它会产生“收敛到错误的极限”。在本文中，我们仔细回顾了正式的理由的方法，确定点，它可能会失败，并得出一个必要的和充分的标准的正确性。然而，这一标准是不实际的，因为它的应用需要检查一个无限的身份之塔。相反，我们提出了一个实际的测试，只涉及检查的前几个身份，这就提出了问题的“敏感性”的测试。这种敏感性以及对失败的可能原因（病因学）的一般见解，然后在两个玩具模型中进行测试，其中正确的答案是已知的。至少在这些模型中，测试工作得很好。
The complex Langevin method is a leading candidate for solving the so-called sign problem occurring in various physical situations. Its most vexing problem is that sometimes it produces ‘convergence to the wrong limit’. In this paper we carefully revisit the formal justification of the method, identifying points at which it may fail and derive a necessary and sufficient criterion for correctness. This criterion is, however, not practical, since its application requires checking an infinite tower of identities. We propose instead a practical test involving only a check of the first few of those identities; this raises the question of the ‘sensitivity’ of the test. This sensitivity as well as the general insights into the possible reasons of failure (the etiology) are then tested in two toy models where the correct answer is known. At least in those models the test works perfectly.