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 inhomogeneity on the mesoscopic scale. In this work, we model this inhomogeneity by real-space fluctuating elasticity with a spatially correlated distribution and calculate the dynamical properties using an exact real-space field theoretical approach. Our results clarify that the excess low-frequency density of states (DOS) originates from a selective scattering effect (stronger scattering of short wavelengths) induced by elastic inhomogeneity. The visualization of the local DOS in real space reveals the existence of anomalous modes, highly excited spots, at low frequencies. The findings regarding these highly excited spots and the selectivity of the correlation length were missed in previous perturbative field approaches in wave-vector space, and they align with recent progress from particle-level simulations and experiments. These results provide concrete insights into the low-frequency vibrational anomaly of amorphous solids from the perspective of simple elastic inhomogeneity.