Wave-packet simulations, regarded as phonon dynamics in the literature, have been used to explore interface conductance problems and to study the frequency-based dynamics of systems of particles. In this work we introduce an extension of the method to improve the postsimulation analysis and to add an energy aspect to the definition of a wave packet. In a wave-packet simulation the most populated frequency activated with the wave packet is known through knowledge of the wave number implemented in the atom displacement equation. The one-to-one correspondence of wave number and frequency is known through the phonon dispersion relation (PDR). We add the temperature dependence of this one-to-one correspondence to the analysis of wave packets through consideration of a temperature-dependent PDR and showed the importance of the temperature-dependent PDR in the wave-packet definition by presenting results considering and neglecting the phenomenon. In addition, the temperature-dependent PDR and the density of states provide us the chance to change the nature of the atomic displacement amplitude as an arbitrary parameter to a tuning knob for the amount of energy it carries and utilize the chance to provide a quantitative measure for the validity of molecular-dynamics simulations considering their classical nature in comparison with the quantum particle picture of phonons.

• Received 24 June 2020
• Revised 29 January 2021
• Accepted 6 April 2021

DOI:https://doi.org/10.1103/PhysRevE.103.043311