Reproducing and Extending Brownian Motion in Optical Trap: A Computational Reimplementation of Volpe and Volpe (2013)

TL;DR

This paper reimplements and extends a 2013 study on Brownian motion in optical traps using Python, validating key physical regimes and adding new force perturbation analyses for educational and research purposes.

Contribution

It provides an independent, computational reimplementation of the 2013 model, extending it to include force perturbations and stochastic resonance for enhanced understanding.

Findings

Validated the transition from ballistic to diffusive motion.

Reproduced optical confinement and velocity autocorrelations.

Extended analysis to include rotational forces and Kramers transitions.

Abstract

We present a re-representation and independent simulation of the model introduced by Giorgio Volpe and Giovanni Volpe in their 2013 study of a Brownian particle in an optical trap (Volpe and Volpe, 2013). Rather than duplicating their original plots, we reconstructed the simulations from first principles using Python, implementing stochastic differential equations via finite difference schemes. This work reproduces and validates the key physical regimes described in the original article, including the transition from ballistic to diffusive motion, optical confinement, and velocity autocorrelations. To simulate rotational forces (Grier, 2003) and Kramers transitions (Haenggi et al., 1990), we also extend the analysis to include force perturbations, rotational fields, Kramers transitions, and stochastic resonance. The simulations provide pedagogical insight into stochastic dynamics and numerical modeling, reinforcing the original study's value as a teaching and research tool in statistical and computational physics.