On the Time Transition Between Short and LongTime Regimes of Colloidal Particles in External Periodic Potentials
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The dynamics of colloidal particles at infinite dilution, under the influence of periodic external potentials, is studied here via experiments and numerical simulations for two representative potentials. From the experimental side, we analyzed the motion of a colloidal tracer in a onedimensional array of fringes produced by the interference of two coherent laser beams, providing in this way an harmonic potential. The numerical analysis has been performed via Brownian dynamics (BD) simulations. The BD simulations correctly reproduced the experimental position and timedependent density of probability of the colloidal tracer in the shorttimes regime. The longtime diffusion coefficient has been obtained from the corresponding numerical mean square displacement (MSD). Similarly, a simulation of a random walker in a one dimensional array of adjacent cages with a probability of escaping from one cage to the next cage is one of the most simple models of a periodic potential, displaying two diffusive regimes separated by a dynamical caging period. The main result of this study is the observation that, in both potentials, it is seen that the critical time (Formula presented.), defined as the specific time at which a change of curvature in the MSD is observed, remains approximately constant as a function of the height barrier (Formula presented.) of the harmonic potential or the associated escape probability of the random walker. In order to understand this behavior, histograms of the first passage time of the tracer have been calculated for several height barriers (Formula presented.) or escape probabilities. These histograms display a maximum at the most likely first passage time (Formula presented.), which is approximately independent of the height barrier (Formula presented.), or the associated escape probability, and it is located very close to the critical time (Formula presented.). This behavior suggests that the critical time (Formula presented.), defining the crossover between short and longtime regimes, can be identified as the most likely first passage time (Formula presented.) as a first approximation. © Copyright © 2021 PérezGuerrero, ArauzLara, SarmientoGómez and GuerreroGarcía.
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external field; long time diffusion; most likely escape time; periodic potential; spherical tracer
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