The Size of a Polymer of String-Bits: A Numerical Investigation

TL;DR

This paper explores how the size of a string modeled as a polymer of point-like constituents is affected by interactions, using simplified models and variational methods to analyze size changes non-perturbatively.

Contribution

It introduces a simplified analog model to study non-perturbative effects of string interactions on size, employing variational techniques for analysis.

Findings

Size depends on interaction strength g

Size varies with number of bits

Simplified model captures key interaction effects

Abstract

In string-bit models, string is described as a polymer of point-like constituents. We attempt to use string-bit ideas to investigate how the size of string is affected by string interactions in a non-perturbative context. Lacking adequate methods to deal with the full complications of bit rearrangement interactions, we study instead a simplified analog model with only ``direct'' potential interactions among the bits. We use the variational principle in an approximate calculation of the mean-square size of a polymer as a function of the number of constituents/bits for various interaction strengths g in three specific models.