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arXiv · 1507.07351

Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method

Kenji Fukushima·Yuya Tanizaki
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Abstract

The Lefschetz thimble method, i.e., the integration along the steepest descent cycles, is an idea to evade 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.

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Kenji Fukushima, Yuya Tanizaki. 2015-07-27. Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method. https://doi.org/10.1093/ptep/ptv152

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