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Explicit propagators for a random walker and unidirectionality on linear chains

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  • Bakalis, Evangelos

Abstract

Explicit propagators are given for a diffusing particle (motor) moving on a linear chain of either infinity or finite length with reflecting ends. Each chain contains a number of thermally accessible barriers and/or potential wells (active sites). All particle interactions with its environment are considered to be short-range and are described by repulsive/attractive delta function potentials. By employing perturbation expansion, closed analytical expressions for the spatio-temporal evolution of the probability density function of the motor are derived, and are valid up to second order with respect to the expansion parameter u, which denotes the strength of interaction between motor and active sites. The mean displacement for two different chains is calculated indicating in both cases that the organization of the motion is done through the interplay of interaction intensities and their positions.

Suggested Citation

  • Bakalis, Evangelos, 2012. "Explicit propagators for a random walker and unidirectionality on linear chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3093-3101.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:11:p:3093-3101
    DOI: 10.1016/j.physa.2012.01.029
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    References listed on IDEAS

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    1. Bakalis, E. & Vlahos, C. & Kosmas, M., 2006. "Diffusion in the presence of a pole: From the continuous Gaussian to a discrete lattice model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 1-16.
    2. David A. Leigh & Jenny K. Y. Wong & François Dehez & Francesco Zerbetto, 2003. "Unidirectional rotation in a mechanically interlocked molecular rotor," Nature, Nature, vol. 424(6945), pages 174-179, July.
    3. Viviana Serreli & Chin-Fa Lee & Euan R. Kay & David A. Leigh, 2007. "A molecular information ratchet," Nature, Nature, vol. 445(7127), pages 523-527, February.
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