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While the quantum scattering theory has provided the theoretical underpinning for phonon interactions, the correspondence between the phonon modes and normal modes of vibrations has never been fully established; for example, the nature of energy exchange during elementary normal mode interactions remains largely unknown. In this work, by adopting a set of real asymmetric normal mode amplitudes, we first discriminate the normal and Umklapp processes directly from atomistic dynamics. We then demonstrate that the undulating harmonic and anharmonic potentials, which allow a number of interaction pathways, generate several total-energy-conserving forward and backward scattering events including those which are traditionally considered as quantum-forbidden. Although the normal mode energy is proportional to the square of the eigen-frequency, we deduce that the energy exchanged from one mode to another in each elementary interaction is proportional to the frequency – a quantum-like restriction. We anticipate that the current approach can be utilized profitably to discover unbiased scattering channels, many traditionally quantum forbidden, with complex anharmonicities. Our discovery will aid in the development of next-generation Peierls-Boltzmann transport simulations that access normal mode scattering pathways from finite temperature  ab initio  simulations.

Deducing Phonon Scattering from Normal Mode Excitations