Scaling Properties of a Moving Polymer
Abstract
We set up an SPDE model for a moving, weakly self-avoiding 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:
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arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2006.07189
- arXiv:
- arXiv:2006.07189
- Bibcode:
- 2020arXiv200607189M
- Keywords:
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- Mathematics - Probability;
- Mathematical Physics;
- 60H15;
- 82D60
- E-Print:
- 37 pages