In the present study a few approaches are developed for theoretical investigation of vibrational energy propagation in highly ordered polymers and linear atomic chains. Density matrix formalism applied to explain the transition between ballistic and diffusive regimes in polymers, the diffusive and ballistic regimes of energy transport are described in terms of asymptotic limits of exact solution of Liouville-Bloch equation. Energy bands theory is developed for oligomeric structures such as perfluoroalkane and alkane compounds, as an example, practical application for understanding experimental data for alkane is discussed. Also, purely electronic torsional mode in linear atomic chains, such as cumulene, is considered. The speed of up to 1000~km/s for electronic sound is predicted, the spectrum of quanta (torsitons) of torsional electronic mode in cumulene is obtained.
