https://doi.org/10.1140/epjs/s11734-024-01194-3
Regular Article
Scaling limits for the generalized Langevin equation via diffusion approximation theory
1
School of Mathematics and Statistics, Northwestern Polytechnical University, 710072, Xi’an, China
2
School of Mathematics, Xi’an University of Finance and Economics, 710100, Xi’an, China
3
Research & Development Institute of Northwestern Polytechnical University in Shenzhen, 518057, Shenzhen, China
4
MOE Key Laboratory of Complexity Science in Aerospace, Northwestern Polytechnical University, 710072, Xi’an, China
Received:
18
March
2024
Accepted:
4
June
2024
Published online:
11
June
2024
This work presents a new method for obtaining the precise stationary state solutions of the Generalized Langevin Equation (GLE). The method combines Mori–Zwanzig formalism and diffusion approximation theory to provide an accurate analytical method for exploring the non-Markovian GLE. We demonstrate that the above-mentioned method can capture well the stationary state solutions of the GLE with memory kernel control and provide a valuable tool for studying the anomalous diffusion events. Numerical simulations confirm the accuracy of such Mori–Zwanzig formalism and diffusion approximation method.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
