Attempt-time Monte Carlo: an alternative for simulation of stochastic jump processes with time-dependent transition rates

TL;DR

This paper introduces an innovative simulation method for Markovian jump processes with time-dependent rates, avoiding complex integral inversions and enabling exact solutions through a Dyson series approach.

Contribution

The paper presents a novel attempt-time Monte Carlo method that efficiently simulates stochastic jump processes with time-dependent transition rates, offering a new exact solution framework.

Findings

Demonstrated effectiveness on interacting two-level systems

Compared favorably to existing methods in accuracy and efficiency

Applicable to periodically driven systems

Abstract

We present a new method for simulating Markovian jump processes with time-dependent transitions rates, which avoids the transformation of random numbers by inverting time integrals over the rates. It relies on constructing a sequence of random time points from a homogeneous Poisson process, where the system under investigation attempts to change its state with certain probabilities. With respect to the underlying master equation the method corresponds to an exact formal solution in terms of a Dyson series. Different algorithms can be derived from the method and their power is demonstrated for a set of interacting two-level systems that are periodically driven by an external field.