Diffusion in the Presence of Scale-Free Absorbing Boundaries

Abstract

Scale-free surfaces, such as cones, remain unchanged under a simultaneous expansion of all coordinates by the same factor. Probability density of a particle diffusing near such absorbing surface at large time approaches a simple form that incorporates power-law dependencies on time and distance from a special point, such as apex of the cone, which are characterized by a single exponent $\eta$. The same exponent is used to describe the number of spatial conformations of long ideal polymer attached to the special point of a repulsive surface of the same geometry and can be used in calculation of entropic forces between such polymers and surfaces. We use the solution of diffusion equation near such surfaces to find the numerical values of $\eta$, as well as to provide some insight into the behavior of ideal polymers near such surfaces.

arXiv comment7 pages, 7 figures

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Cited by in corpus (7)

• Anomalous Dimension in a Two-Species Reaction-Diffusion System
• Long Polymers Near Wedges and Cones
• Attractive and repulsive polymer-mediated forces between scale-free surfaces
• Quantum particle in a spherical well confined by a cone
• Pinning and unbinding of (ideal) polymers from a wedge corner
• Localization of random walks to competing manifolds of distinct dimensions
• Nonequilibrium interactions between ideal polymers and a repulsive surface