Two-dimensional optical thermal ratchets based on Fibonacci spirals

Ke Xiao, Yael Roichman, David G. Grier

    Research output: Contribution to journalArticlepeer-review


    An ensemble of symmetric potential energy wells arranged at the vertices of a Fibonacci spiral can serve as the basis for an irreducibly two-dimensional thermal ratchet. Periodic rotation of the potential energy landscape through a three-step cycle drives trapped Brownian particles along spiral trajectories through the pattern. Which spiral is selected depends on the angular displacement at each step, with transitions between selected spirals arising at rational proportions of the golden angle. Fibonacci spiral ratchets therefore display an exceptionally rich range of transport properties, including inhomogeneous states in which different parts of the pattern induce motion in different directions. Both the radial and angular components of these trajectories can undergo flux reversal as a function of the scale of the pattern or the rate of rotation.

    Original languageEnglish (US)
    Article number011131
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Issue number1
    StatePublished - Jul 22 2011

    ASJC Scopus subject areas

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


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