On the path integral simulation of space-time fractional Schroedinger equation with time independent potentials

• URL: http://arxiv.org/abs/2306.14333v1
• Date: Sun, 25 Jun 2023 20:14:40 GMT
• Title: On the path integral simulation of space-time fractional Schroedinger equation with time independent potentials
• Authors: Sumita Datta and Radhika Prosad Datta
• Abstract summary: A Feynman-Kac path integral method has been proposed for solving the Cauchy problems associated with the space-time fractional Schroedinger equations. We have been able to simulate the space-time fractional diffusion process with comparable simplicity and convergence rate as in the case of a standard diffusion.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work a Feynman-Kac path integral method based on Levy measure has been proposed for solving the Cauchy problems associated with the space-time fractional Schroedinger equations arising in interacting systems in fractional quantum mechanics. The Continuous Time Random Walk(CTRW) model is used to simulate the underlying Levy process-a generalized Wiener process. Since we are interested to capture the lowest energy state of quantum systems, we use Pareto distribution as opposed to Mittag-Leffler random variables, which are more suitable for finite time. Adopting the CTRW model we have been able to simulate the space-time fractional diffusion process with comparable simplicity and convergence rate as in the case of a standard diffusion. We hope this paves an elegant way to solve space-time diffusion equations numerically through Fractional Feynman-Kac path integral technique as an alternative to fractional calculus.

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