Multifractality of Brownian motion near absorbing polymers

TL;DR

This paper investigates the multifractal properties of Brownian motion near absorbing polymers, using field theory and renormalization group methods to derive and evaluate the multifractal spectrum.

Contribution

It introduces a novel field-theoretic approach to characterize the multifractal behavior of Brownian motion around absorbing polymers.

Findings

Multifractal spectra exhibit convexity properties typical of multifractal scaling.

Asymptotic series for the multifractal spectrum are obtained and resummed.

The approach links higher moments of the Laplacian field to composite operators in field theory.

Abstract

We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi^4-field theory relating higher moments of the Laplacian field of Brownian motion to corresponding composite operators. The resulting spectra of scaling dimensions of these operators display the convexity properties which are necessarily found for multifractal scaling but unusual for power of field operators in field theory. Using a field-theoretic renormalization group approach we obtain the multifractal spectrum for absorbtion at the core of a polymer star as an asymptotic series. We evaluate these series using resummation techniques.