Half- and full-integer power law for distance fluctuations: Langevin dynamics in one- and two-dimensional systems

Langevin dynamics of one- and two-dimensional systems with the nearest neighbor couplings is examined to derive the autocorrelation function (ACF) of the distance fluctuations. Understanding of the dynamics of pairwise distance correlation is essential in the studies using single-molecule spectroscopy. For both 1-D cases of an open chain and a closed loop, a power law of t−1/2, t−3/2 and t−5/2 for the ACF are obtained, and for 2-D systems of a sheet and a tube, a power law of t−1, t−2 and t−3 are found. The different exponent of the power law is shown to depend on the location of the pairwise beads and their topography.