  Logarithmic oscillations superimposed on a power-law trend appear in the
behavior of various complex hierarchical systems. In this paper, we study the
logarithmic oscillations of relaxation curves in p-adic diffusion models that
are used to describe the conformational dynamics of protein. We consider the
case of a purely p-adic diffusion, as well as the case of p-adic diffusion with
a reaction sink. We show that, relaxation curves for large times in these two
cases are described by a power law on which logarithmic oscillations are
superimposed whose period and amplitude are determined by the parameters of the
model. We also provide a physical explanation of the emergence of oscillations
in relaxation curves and discuss the relation of the results to the experiments
on relaxation dynamics of protein.
