Particle dynamics in viscoelastic media: Effects of non-thermal white noise on barrier crossing rates

The growing interest in the dynamics of self-driven particle motion has brought increased attention to the effects of non-thermal noise on condensed phase diffusion. Thanks to data recently collected by Ferrer et al. on activated dynamics in the presence of memory [Phys. Rev. Lett. 126, 108001 (2021)], some of these effects can now be characterized quantitatively. In the present paper, the data collected by Ferrer et al. are used to calculate the extent to which non-thermal white noise alters the time taken by single micron-sized silica particles in a viscoelastic medium to cross the barrier separating the two wells of an optically created bistable potential. The calculation-based on a generalized version of Kramers's flux-over-population approach-indicates that the added noise causes the barrier crossing rate (compared to the noise-free case) to first increase as a function of the noise strength and then to plateau to a constant value. The precise degree of rate enhancement may depend on how the data from the experiments conducted by Ferrer et al. are used in the flux-over-population approach. As claimed by Ferrer et al., this approach predicts barrier crossing times for the original silica-fluid system that agree almost perfectly with their experimental counterparts. However, this near-perfect agreement between theory and experiment is only achieved if the theoretical crossing times are obtained from the most probable values of a crossing time distribution constructed from the distributions of various parameters in Kramers's rate expression. If the mean values of these parameters are used in the expression instead, as would be commonly done, the theoretical crossing times are found to be as much as 1.5 times higher than the experimental values. However, these times turn out to be consistent with an alternative model of viscoelastic barrier crossing based on a mean first passage time formalism, which also uses mean parameter values in its rate expression. The rate enhancements predicted for barrier crossing under non-thermal noise are based on these mean parameter values and are open to experimental verification.