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

Datta Sumita (), Datta Radhika Prosad () and Rejcek James M. ()
Additional contact information
Datta Sumita: Department of Pure and Applied Mathematics, Alliance University, Bengaluru 562106, India; and Department of Physics, The University of Texas at Arlington, Texas 76019, USA
Datta Radhika Prosad: Indian Institute of Foreign Trade (IIFT), Kolkata Campus, Kolkata 700107, India
Rejcek James M.: Department of Physics, The University of Texas at Arlington, Arlington, TX 76019, USA

Monte Carlo Methods and Applications, 2025, vol. 31, issue 3, 189-205

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.

Keywords: Feynman–Kac path integral method; Lévy process; Riesz derivatives; continuous time random walk; Caputo derivatives (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/mcma-2025-2011 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:31:y:2025:i:3:p:189-205:n:1002

Ordering information: This journal article can be ordered from
https://www.degruyte ... ournal/key/mcma/html

DOI: 10.1515/mcma-2025-2011

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().