On the Generalized Borel Transform and its Application to the Statistical Mechanics of Macromolecules

TL;DR

The paper introduces the Generalized Borel Transform (GBT), a new integral transform, and demonstrates its effectiveness in deriving exact statistical properties of macromolecules within the Random Flight Model, simplifying calculations in polymer physics.

Contribution

It presents the GBT and applies it to the RFM, providing exact expressions for the polymer propagator and highlighting its mathematical simplicity and broader applicability.

Findings

Exact expression for the polymer propagator derived using GBT

Simplifies computation of distribution functions in polymer models

Applicable to various polymer topologies

Abstract

We present a new integral transform called the Generalized Borel Transform (GBT) and show how to use it to compute some distribution functions used to describe the statistico-mechanical behavior of macromolecules. For this purpose, we choose the Random Flight Model (RFM) of macromolecules and show that the application of the GBT to this model leads to the exact expression of the polymer propagator (two-point correlation function) from which all the statistical properties of the model can be obtained. We also discuss the mathematical simplicity of the GBT and its applicability to polymers with other topologies.