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Stable solvers for real-time Complex Langevin

A preprint version of the article is available at arXiv.


This study explores the potential of modern implicit solvers for stochastic partial differential equations in the simulation of real-time complex Langevin dynamics. Not only do these methods offer asymptotic stability, rendering the issue of runaway solution moot, but they also allow us to simulate at comparatively large Langevin time steps, leading to lower computational cost. We compare different ways of regularizing the underlying path integral and estimate the errors introduced due to the finite Langevin time steps. Based on that insight, we implement benchmark (non-)thermal simulations of the quantum anharmonic oscillator on the canonical Schwinger-Keldysh contour of short real-time extent.


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Correspondence to Daniel Alvestad.

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Alvestad, D., Larsen, R. & Rothkopf, A. Stable solvers for real-time Complex Langevin. J. High Energ. Phys. 2021, 138 (2021).

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  • Lattice Quantum Field Theory
  • Stochastic Processes