 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-312/4/d/solution

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

The

ℓ = 2

projection of the Boltzmann hierarchy is

Θ_{2}^{'} = \frac{k}{5} (2 Θ_{1} - 3 Θ_{3}) - Γ Θ_{2} .

In tight coupling,

Θ_{2} = O (k /Γ)

and

Θ_{3}

is higher order. Neglecting

Θ_{2}^{'}

relative to

Γ Θ_{2}

at leading order gives

Θ_{2} ≃ \frac{2}{5} \frac{k}{Γ} Θ_{1},

C = 2/5

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