The damped wave equation and associated polymer

TL;DR

This paper studies a damped wave equation driven by Gaussian noise and introduces a related weakly self-avoiding polymer, showing it has an effective radius scaling as J^{5/3}.

Contribution

It establishes a connection between the damped wave SPDE and a new polymer model, analyzing its spatial properties.

Findings

Polymer's effective radius scales as J^{5/3}.

Existence of a stationary mild solution to the SPDE.

Introduction of a novel polymer model linked to the SPDE.

Abstract

Considering the damped wave equation with a Gaussian noise $F$ where $F$ is white in time and has a covariance function depending on spatial variables, we will see that this equation has a mild solution which is stationary in time $t$. We define a weakly self-avoiding polymer with intrinsic length $J$ associated to this SPDE. Our main result is that the polymer has an effective radius of approximately $J^{5/3}$.