  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.
