Kernel controlled real-time Complex Langevin simulation

TL;DR

This paper introduces a kernel-based method to improve the convergence of complex Langevin simulations for real-time quantum dynamics, enabling simulations of previously inaccessible regimes.

Contribution

The authors develop a systematic scheme to find kernels that restore correct convergence in complex Langevin simulations of quantum real-time dynamics.

Findings

Successfully simulated up to 1.5β on the Schwinger-Keldysh contour

Demonstrated kernel scheme's ability to restore convergence

Extended complex Langevin applicability to challenging parameter regimes

Abstract

This study explores the utility of a kernel in complex Langevin simulations of quantum real-time dynamics on the Schwinger-Keldysh contour. We give several examples where we use a systematic scheme to find kernels that restore correct convergence of complex Langevin. The schemes combine prior information we know about the system and the correctness of convergence of complex Langevin to construct a kernel. This allows us to simulate up to $1.5\beta$ on the real-time Schwinger-Keldysh contour with the $0+1$ dimensional anharmonic oscillator using $m=1,\lambda=24$, which was previously unattainable using the complex Langevin equation.