 Solution

ID: past-exam-of-the-quantum-condensed-matter-course-of-the-university-of-cambridge/2008/section-a/a3/c/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

For the convention

γ = Re (γ_{0} e^{iω t})

G^{*} = iω \int_{0}^{\infty} G (t) e^{- iω t} d t

. Thus

G^{*} = \frac{iω η}{1 + iω τ}, G^{'} = G_{0} \frac{( ω τ ) ^{2}}{1 + ( ω τ ) ^{2}}, G^{''} = G_{0} \frac{ω τ}{1 + ( ω τ ) ^{2}} .

ω τ > 1

, so the response is predominantly solid-like above the crossover

ω_{c} = 1/ τ, f_{c} = 1/ (2 π τ) .

G^{*} ≃ iω η

G^{*} \to G_{0}

 New to topics? Read the docs here!