Abstract
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.
Highlights
Normal modes are non-interacting, non-decaying collective excitations of atomic vibrations – these are the eigen-states of the interacting harmonic Hamiltonian
The final limitation on the correspondence between the normal modes and phonon modes is right at the heart of quantum mechanics in that the energy transfer between quantum objects is always proportional to the corresponding frequencies, but the nature of energy exchange during elementary normal mode interactions remains largely unknown
We show that the theoretical limitation of the traditional normal mode analysis (NMA) analyses can be removed by adopting a set of real asymmetric normal mode amplitudes, which can distinguish lattice waves moving in opposite wave vector directions – a virtue that immediately endows the ability to discriminate N and U processes and the phase space associated with their interactions
Summary
Normal modes are non-interacting, non-decaying collective excitations of atomic vibrations – these are the eigen-states of the interacting harmonic Hamiltonian. A key assumption in deriving the transition rates is that the anharmonic Hamiltonians add only small perturbations, and higher order contributions get progressively weaker. This assumption has been examined recently from two angles. We show that the theoretical limitation of the traditional NMA analyses can be removed by adopting a set of real asymmetric normal mode amplitudes, which can distinguish lattice waves moving in opposite wave vector (i.e. in +q and −q) directions – a virtue that immediately endows the ability to discriminate N and U processes and the phase space associated with their interactions (see Methods section). Using controlled cubic and quartic anharmonicity, we infer that the energy transferred from one normal mode to another in an elementary interaction is proportional to the corresponding frequencies – a surprising similarity to energy interchanges at the quantum level
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