Past exam of the quantum condensed matter course of the University of Cambridge / 2008 / Section A / A3 / c / Solution

For the convention $\gamma =\mathrm{Re}({\gamma }_0{e}^{i\omega t})$, the complex viscoelastic modulus is $G^{\ast }=i\omega {\int }_0^{\infty }G(t)e^{-i\omega t}dt$. ThusThe storage modulus exceeds the loss modulus for $\omega \tau >1$, so the response is predominantly solid-like above the crossoverAt low frequency $G^{\ast }\simeq i\omega \eta$; at high frequency $G^{\ast }\to G_0$.