Fractons in proteins: Can they lead to anomalously decaying timeautocorrelations?

Motivated by recent studies on the fractal nature of folded proteins, we analyze the time-dependent autocorrelation function ⟨→x(t)⋅→x(0)⟩
of the distance between two points on a thermally vibrating fractal. Using fractons, the vibrational excitations of a fractal, we show that for both strongly underdamped and overdamped vibrations this correlation function decays anomalously, displaying a crossover from a nearly stretched exponential decay at short times to a slow algebraic decay at long times. Relationship to single molecule experiments is discussed.