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arXiv · 2410.12762

Computing real-time quantum path integrals on Sewed, almost-Lefschetz thimbles

Zong-Gang Mou·Paul M. Saffin·Anders Tranberg
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Abstract

We present a method to compute real-time path integrals numerically, by Monte-Carlo sampling on near-Lefschetz thimbles. We present a collection of tools based on the Lefschetz thimble methods, which together provide an alternative to existing methods such as the Generalised thimble. These involve a convenient coordinate parameterization of the thimble, direct numerical integration along a radial coordinate into an effective path integral weight and locally deforming the Lefschetz thimble using its Gaussian (non-interacting theory) counterpart in a region about the critical point. We apply this to quantum mechanics, identify possible pitfalls and benefits, and benchmark its efficiency.

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Zong-Gang Mou, Paul M. Saffin, Anders Tranberg. 2024-10-16. Computing real-time quantum path integrals on Sewed, almost-Lefschetz thimbles. https://arxiv.org/abs/2410.12762

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