Theory of Phonon Mode Interactions from Current Correlations and Applications in Disordered Solids and Liquids

Phonons are characterized by the normal modes of vibration that arise from the motion of the atoms in a periodic lattice. Traditionally, the theoretical treatment involves solving the dynamical matrix to obtain the normal modes and their respective dispersion relations. This approach fails for disordered solids and liquids when there is a complete breakdown of translational symmetry even when there is a well-identifiable dispersion relationship for such systems. In this work, we propose a new approach that makes use of the spatial Fourier component of the particle current (or momenta) to obtain the dispersion relationship without directly working with the dynamical matrix. By Taylor expanding the particle current with respect to the atomic displacements and without invoking a repeating unit cell, we first demonstrate that the leading term corresponds to the normal modes of vibration. We then show that higher orders of the current expansion correspond to the scattering of normal modes in anharmonic systems. Along with a new theoretical approach, we will present results from atomistic simulations that highlight the attractiveness of the particle current approach in disordered solids and liquids.