 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/33b/b/iv/solution

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

γ_{A} = (1 - g^{2})^{2} + g^{4} + O (g^{3}) = 1 - 2 g^{2} + O (g^{3}) = 1 - \frac{λ ^{2}}{8 ω ^{4}} + O (λ^{3}) .

The displayed truncation lies between zero and one when

∣ λ ∣ \leq 22 ω^{2}

. Perturbation theory requires the stronger condition

∣ λ ∣ ≪ ω^{2}

; the exact coupled oscillator is stable only for

∣ λ ∣ < ω^{2}

. The reduction in purity records entanglement between

A

and

B

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