Stable solvers for real-time Complex Langevin

TL;DR

This paper investigates the use of modern implicit solvers for stochastic PDEs in real-time complex Langevin simulations, demonstrating improved stability and efficiency for quantum systems like the anharmonic oscillator.

Contribution

It introduces the application of implicit solvers to complex Langevin dynamics, enabling larger time steps and reducing computational costs in real-time quantum simulations.

Findings

Implicit solvers provide asymptotic stability in complex Langevin simulations.

Larger Langevin time steps are feasible, lowering computational costs.

Benchmark simulations of quantum anharmonic oscillator validate the approach.

Abstract

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 largeLangevin 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. 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.