Fluctuation force exerted by a planar self-avoiding polymer

TL;DR

This paper derives the fluctuation-induced force exerted by a planar self-avoiding polymer on objects within 2D domains using Schramm Loewner evolution, exploring stability and extensions to various interfaces.

Contribution

It provides a novel analytical expression for fluctuation forces exerted by polymers in 2D geometries using SLE, including multiple polymers and boundary interactions.

Findings

Derived force expressions for single and multiple polymers

Analyzed stability of objects under fluctuation forces

Extended results to various SLE interfaces like Ising and percolation

Abstract

Using results from Schramm Loewner evolution (SLE), we give the expression of the fluctuation-induced force exerted by a polymer on a small impenetrable disk, in various 2-dimensional domain geometries. We generalize to two polymers and examine whether the fluctuation force can trap the object into a stable equilibrium. We compute the force exerted on objects at the domain boundary, and the force mediated by the polymer between such objects. The results can straightforwardly be extended to any SLE interface, including Ising, percolation, and loop-erased random walks. Some are relevant for extremal value statistics.