 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-353/3/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The deterministic relaxation matrix is

R (q) = (M q^{2} (a + κ q^{2}) Γ c M c q^{2} Γ (\overset{a}{ˉ} + \overset{κ}{ˉ} q^{2})) .

A_{q} = a + κ q^{2}

and

B_{q} = \overset{a}{ˉ} + \overset{κ}{ˉ} q^{2}

, their decay rates obey

(λ - M q^{2} A_{q}) (λ - Γ B_{q}) - M Γ c^{2} q^{2} = 0 .

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