Perturbative theory for Brownian vortexes

Henrique W. Moyses, Ross O. Bauer, Alexander Y. Grosberg, David G. Grier

    Research output: Contribution to journalArticlepeer-review


    Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers.

    Original languageEnglish (US)
    Article number062144
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Issue number6
    StatePublished - Jun 30 2015

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Condensed Matter Physics


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