Directed lines in sparse potentials

T. J. Newman, A. J. McKane

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    4 Citations (Scopus)


    We present a continuum formulation of a (d + 1)-dimensional directed line interacting with sparse potentials (i.e., d-dimensional potentials defined only at discrete longitudinal locations.) An iterative solution for the partition function is derived. The impulsive influence of the potentials induces discontinuities in the evolution of the probability density P(x,t) of the directed line. The effects of these discontinuities are studied in detail for the simple case of a single defect. We then investigate sparse columnar potentials defined as a periodic array of defects in (2+1) dimensions, and solve exactly for P. A nontrivial binding-unbinding transition is found.
    Original languageEnglish
    Pages (from-to)165-175
    Number of pages11
    JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
    Issue number1
    Publication statusPublished - Jan 1997


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