Propagating vibrational excitations in molecular chains

We investigate quantum dynamics of vibrational excitations in one-dimensional (1D) molecular chain. Our model includes nearest neighbor interaction between identical molecular sites and one impurity atom placed in the middle ($n=0$). We show that upon exciting the impurity site, its excess energy for relatively long for molecular scales time up to 100 ps is not redistributed uniformly among all other degrees of freedom. On the contrary an excitation propagates along the chain, reflected from the chain ends, and quantum interference of these waves yields to recurrence cycles and echo phenomena. For a critical cycle number $k_c$, echo components of the neighboring cycles start to overlap, and eventually for $k \gg k_c$ dynamics looks like chaotic one. The critical cycle number $k_c$ depends on the coupling strength $0 \leq C \leq 1$ of the impurity site with its neighbors $n = \pm 1$. $k_c$ achieves the maximum for $C^2 = 1/2$. Our results are in qualitative agreement with experimental data on vibrational excitations in various (CH$_2)_n$ molecular chains, and besides offer a way for loss-free energy transfer between separated in space reaction centers.