Gaussian polymer chains in a harmonic potential: The path integral approach

TL;DR

This paper develops a path integral method to analyze Gaussian polymer chains under harmonic confinement, deriving the gyration radius distribution and validating results with Monte Carlo simulations.

Contribution

It introduces a novel path integral approach to compute the gyration radius distribution of polymers in harmonic potentials, combining analytical and numerical methods.

Findings

Analytical expression for gyration radius distribution derived

Monte Carlo simulations confirm theoretical predictions

Good agreement between theory and simulations across various external fields

Abstract

We study conformations of the Gaussian polymer chains in d-dimensional space in the presence of an external field with the harmonic potential. We apply a path integral approach to derive an explicit expression for the probability distribution function of the gyration radius. We calculate this function using Monte Carlo simulations and show that our numerical and theoretical results are in a good agreement for different values of the external field.