Impact of elastic inhomogeneity on collective dynamical properties investigated by field theoretical description in real space

Interpreting the vibrational properties of amorphous solids beyond Debye's theory is challenging due to the presence of mesoscopic scale inhomogeneity. In this work, we model this inhomogeneity using a real space fluctuating elasticity field with a spatially correlated distribution, and investigate the resulting dynamical properties via a real space field theoretic approach. Our two dimensional results indicate that the excess low-frequency density of states (DOS) arises from a selective scattering effect specifically, the stronger scattering of short wavelength modes within the framework of inhomogeneous elasticity. Visualization of the local DOS in real space reveals the existence of anomalous modes, appearing as highly excitable spots at low frequencies. These features, including the role of the correlation length in mode selectivity, were not captured by previous perturbative field theories in wave vector space. Our findings are consistent with recent progress from particle level simulations and experiments in two dimensions, offering concrete insights into the low frequency vibrational anomalies of amorphous solids from the perspective of simple elastic inhomogeneity.