This study explores the potential of modern implicit solvers for stochastic partial differential equations in simulation real-time complex Langevin dynamics. Not only do these methods offer asymptotic stability, rendering issue runaway solution moot, but they also allow us to simulate at comparatively largeLangevin time steps, leading lower computational cost. We compare different ways regulari...

In this paper, we show that the problem of computing the complex roots of unity is not as simple as it seems at rst. In particular, the formulas given in a standard programmer's reference book Knuth, Seminumerical Algorithms, 1981] are shown to be numerically unstable, giving unacceptably large error for moderate sized sequences. We give alternative formulas, which we show to be superior both b...