Transitioning from underdamped to overdamped behavior in theory and in Langevin simulations of desorption of a particle from a Lennard-Jones potential

A Travitz and E Mani and RG Larson, JOURNAL OF RHEOLOGY, 65, 1235-1243 (2021).

DOI: 10.1122/8.0000177

We investigate the transition between the overdamped and underdamped regimes in Langevin dynamics simulations with significant conservative forces by comparing direct simulations with theories of Kramers, Mel'nikov and Meshkov (MM), and Larson and Lightfoot (LL). The need for clarification is made evident by noting that the most commonly cited theories of Kramers and MM do not apply in the overdamped limit to escape times from a Lennard-Jones (LJ) potential, because Kramers and MM do not account for the flatness of the LJ potential at the escape position, which allows for a region of nearly free Brownian diffusion near the escape position. While the little-known LL approach does consider an LJ potential, it does not properly consider the underdamped regime, and so a complete description is only achieved by combining the LL and MM results into a single general equation, which we validate for the first time by an explicit comparison with Langevin simulations.

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