Scaling Properties of a Moving Polymer
Abstract
We set up an SPDE model for a moving, weakly selfavoiding polymer with intrinsic length $J$ taking values in $(0,\infty)$. Our main result states that the effective radius of the polymer is approximately $J^{5/3}$; evidently for large $J$ the polymer undergoes stretching. This contrasts with the equilibrium situation without the time variable, where many earlier results show that the effective radius is approximately $J$. For such a moving polymer taking values in $\mathbf{R}^2$, we offer a conjecture that the effective radius is approximately $J^{5/4}$.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 DOI:
 10.48550/arXiv.2006.07189
 arXiv:
 arXiv:2006.07189
 Bibcode:
 2020arXiv200607189M
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 60H15;
 82D60
 EPrint:
 37 pages