Using a lattice-based Monte Carlo code for simulating self-avoiding flexible
polymers in three dimensions in the absence of explicit hydrodynamics, we study
their Rouse modes. For self-avoiding polymers, the Rouse modes are not expected
to be statistically independent; nevertheless, we demonstrate that numerically
these modes maintain a high degree of statistical independence. Based on
high-precision simulation data we put forward an approximate analytical
expression for the mode amplitude correlation functions for long polymers. From
this, we derive analytically and confirm numerically several scaling properties
for self-avoiding flexible polymers, such as (i) the real-space end-to-end
distance, (ii) the end-to-end vector correlation function, (iii) the
correlation function of the small spatial vector connecting two nearby monomers
at the middle of a polymer, and (iv) the anomalous dynamics of the middle
monomer. Importantly, expanding on our recent work on the theory of polymer
translocation, we also demonstrate that the anomalous dynamics of the middle
monomer can be obtained from the forces it experiences, by the use of the
fluctuation-dissipation theorem.Comment: 16 pages (double spaced), 5 figures, small changes and corrections,
to appear in J. Chem. Phy