A link between anomalous viscous loss and boson peak in soft jammed solids

Soft jammed solids exhibit intriguing mechanical properties, while their linear response is elusive. In particular, foams and emulsions generally reveal anomalous viscous loss with the loss and storage modulus following $G^{\prime \prime} \propto \sqrt{\omega}$ and $G^{\prime} \propto \omega^0$. In this study, we offer a comprehensive microscopic understanding of this behavior. Using microrheology experiment, we measured $G^* = G^{\prime} + i G^{\prime \prime}$ of concentrated emulsions in a wide range of frequencies. In theory, we applied a linear response formalism for microrheology to a soft sphere model that undergoes the jamming transition. We find that the theory quantitatively explains the experiments without the need for parameter adjustments. Our analysis reveals that the anomalous viscous loss results from the boson peak, which is a universal vibrational property of amorphous solids and reflects the marginal stability in soft jammed solids. We discuss that the anomalous viscous loss is universal in systems with various interparticle interactions as it stems from the universal boson peak, and it even survives below the jamming density where thermal fluctuation is pronounced and the dynamics becomes inherently nonlinear.