arXiv subjects

Brandon R. Ferrer

Publications and source records attributed to Brandon R. Ferrer.

5 recordsLinked to original sources

arXiv2026

First-passage time distribution of a Brownian particle harmonically confined in a viscoelastic bath

We investigate theoretically and experimentally the first passage-time properties of a spherical Brownian particle that is harmonically trapped at thermal equilibrium in a fluid at constant temperature. By using the overdamped version of the generalized Langevin equation, we derive a general expression for the probability density function of the time that the particle takes to reach for the first time the minimum of the potential starting from an arbitrary position. We show that such a first-passage time distribution can be implicitly expressed in terms of the friction memory kernel that encodes the interaction of the particle with its surroundings, and correctly reduces to previously found expressions in the case of a Markovian viscous bath. We validate our theoretical results by measuring the first-passage time of colloidal beads optically trapped in non-Markovian baths such as viscoelastic polymer and micellar solutions, as well as in a viscous glycerol/water mixture and water, which behave as Markovian media, having quantitative agreement with the derived expressions. In particular, we find that the mean first-passage time in a viscoelastic bath can surpass that in a viscous medium of the same zero-shear viscosity due to the emergence of slowly decaying tails in the first-passage time probability density of the former.

cond-mat.stat-mech↗

arXiv2024

Transition path time over a barrier of a colloidal particle in a viscoelastic bath

We experimentally study the statistics of the transition path time taken by a submicron bead to successfully traverse an energy barrier created by two optical tweezers in two prototypical viscoelastic fluids, namely, aqueous polymer and micellar solutions. We find a very good agreement between our experimental distributions and a theoretical expression derived from the generalized Langevin equation for the particle motion. Our results reveal that the mean transition path time measured in such viscoelastic fluids have a non-trivial dependence on the barrier curvature and they can be significantly reduced when compared with those determined in Newtonian fluids of the same zero-shear viscosity. We verify that the decrease of the mean transition path time can be described in terms of an effective viscosity that quantitatively coincides with that measured by linear microrheology at a frequency determined by the reactive mode that gives rise to the unstable motion over the barrier. Therefore, our results uncover the linear response of the particle during its thermally activated escape from a metastable state even when taking place in a non-Markovian bath.

cond-mat.soft↗

arXiv2024

Experimental measurement of mean transition path velocities of colloidal particles surmounting energy barriers

Transition paths are rare events occurring when a system, thanks to the effect of fluctuations, crosses successfully from one stable state to another by surmounting an energy barrier. Even though they are of great significance in many mesoscale processes, their direct determination is often challenging due to their short duration as compared to other relevant time-scales. Here, we measure the local average velocity along transition paths of a colloidal bead embedded in a glycerol/water mixture that hops over a barrier separating two optical potential wells. Owing to the slow dynamics of the bead in this viscous medium, we can spatially resolve the mean velocity profiles of the transition paths for distinct potentials, which agree with theoretical predictions of a model for the motion of a Brownian particle traversing a parabolic barrier. This allows us to experimentally verify various expressions linking the behavior of such mean velocities with equilibrium and transition path position distributions, mean transition-path times and mean escape times from the wells. We also show that artifacts in the mean velocity profiles arise when reducing the experimental time resolution, thus highlighting the importance of the sampling rate in the characterization of the transition path dynamics. Our results confirm that mean transition path velocity establishes a fundamental relationship between mean transition path times and equilibrium rates in thermally activated processes of small-scaled systems.

cond-mat.soft↗

arXiv2023

Stochastic energetics of a colloidal particle trapped in a viscoelastic bath

We investigate the statistics of the fluctuations of the energy transfer between an overdamped Brownian particle, whose motion is confined by a stationary harmonic potential, and a surrounding viscoelastic fluid at constant temperature. We derive an analytical expression for the probability density function of the energy exchanged with the fluid over a finite time interval, which implicitly involves the friction memory kernel that encodes the coupling with such a non-Markovian environment, and reduces to the well known expression for the heat distribution in a viscous fluid. We show that, while the odd moments of this distribution are zero, the even moments can be explicitly expressed in terms of the auto-correlation function of the particle position, which generally exhibits a non-mono-exponential decay when the fluid bath is viscoelastic. Our results are verified by experimental measurements for an optically-trapped colloidal bead in semidilute micellar and polymer solutions, finding and excellent agreement for all time intervals over which the energy exchange takes place.

cond-mat.stat-mech↗

arXiv2021

Fluid viscoelasticity triggers fast transitions of a Brownian particle in a double well optical potential

Thermally activated transitions are ubiquitous in nature, occurring in complex environments which are typically conceived as ideal viscous fluids. We report the first direct observations of a Brownian bead transiting between the wells of a bistable optical potential in a viscoelastic fluid with a single long relaxation time. We precisely characterize both the potential and the fluid, thus enabling a neat comparison between our experimental results and a theoretical model based on the generalized Langevin equation. Our findings reveal a drastic amplification of the transition rates compared to those in a Newtonian fluid, stemming from the relaxation of the fluid during the particle crossing events.

cond-mat.soft↗