Size distribution of ring polymers.
We present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For non-interacting and local-interaction models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively, and are shown to be identical in dimension d ≥ 2, albeit with pronounced finite size effects at the critical dimension, d = 2. A symmetry of the problem reveals that dimension d and 4 - d are equivalent, thus the celebrated Airy distribution describing the areal distribution of the d = 1 Brownian excursion describes also a polymer in three dimensions. For a self-avoiding polymer in dimension d we find numerically that the fluctuations of the scaled averaged distance are nearly identical in dimension d = 2, 3 and are well described to a first approximation by the non-interacting excursion model in dimension 5.
Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel.|Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel.
Shlomi
S
Medalion
Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel.|Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel.
Erez
E
Aghion
Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel.
Hagai
H
Meirovitch
Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel.|Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel.
Eli
E
Barkai
Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel.
David A
DA
Kessler