On the applicability of Feynman–Kac path integral simulation to space-time fractional Schrödinger equations

Abstract In this study, we explore the applicability of the Feynman–Kac (FK) path integral formula to space-time fractional Schrödinger equations. In this work, a FK method based on the Lévy measure has been proposed for solving the Cauchy problems associated with the space-time fractional Schrödinger equations arising in interacting quantum systems. Application of an uncoupled Continuous Time Random Walk (CTRW) model with an exponentially distributed waiting time makes the underlying stochastic process a Lévy process which is basically a generalized Wiener process. Since these processes are Markovian in nature we can adopt the classical FK approach to simulate the CTRW model for solving the space-time fractional diffusion process with comparable simplicity and convergence rate as in the case of standard diffusion processes. Our findings underscore the viability of employing the Fractional Feynman–Kac path integral technique as an effective numerical method for solving space-time diffusion equations, thereby offering a promising alternative to traditional fractional calculus approaches.