https://doi.org/10.1140/epjp/s13360-025-06833-9
Regular Article
Reproducing and extending Brownian motion in optical traps: a computational reimplementation of Volpe and Volpe (2013)
Department of Physics, International University of Africa, Khartoum, Sudan
Received:
8
August
2025
Accepted:
5
September
2025
Published online:
22
September
2025
We present an independent computational reimplementation of the model for Brownian motion in an optical trap, originally introduced by Volpe and Volpe (Am J Phys 81(3):224–230, 2013). Using an Euler–Maruyama finite difference scheme to integrate the Langevin equation in Python, we successfully reproduce key results including the transition from ballistic to diffusive motion, optical confinement, and velocity autocorrelation decay. Our implementation provides a quantitative validation of the original work. Furthermore, we extend the analysis to include rotational forces (Grier in Nature 424:810–816, 2003), Kramers transitions in a double-well potential (Hänggi et al. in Rev Mod Phys 62(2):251–341, 1990), and stochastic resonance. This study serves as a transparent, pedagogical resource, providing full code and a critical discussion on numerical methods for stochastic dynamics in computational physics education. The core trade-off of our chosen method clarity and simplicity versus the higher accuracy of advanced integrators is explicitly addressed.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
