Kernel controlled real-time Complex Langevin simulation

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.Comment: 6 pages, 3 figures, talk given at the XVth Quark confinement and the Hadron spectrum conference, Aug. 1st - 6th, 2022, Stavanger, Norway. Date of presentation Aug. 1st 202