 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2026

Paper 353

The functional derivatives are
$$
\frac{\delta F}{\delta\phi}=a\phi+c\psi-\kappa\nabla^2\phi,
\qquad
\frac{\delta F}{\delta\psi}=\bar a\psi+c\phi-\bar\kappa\nabla^2\psi.
$$
With the stated Fourier convention,
$$
\boxed{\dot\phi_{\mathbf q}
=-Mq^2[(a+\kappa q^2)\phi_{\mathbf q}+c\psi_{\mathbf q}]
-i\sqrt{2M}\,\mathbf q\cdot\boldsymbol\Lambda_{\mathbf q}},
$$
$$
\boxed{\dot\psi_{\mathbf q}
=-\Gamma[(\bar a+\bar\kappa q^2)\psi_{\mathbf q}
+c\phi_{\mathbf q}]+\sqrt{2\Gamma}\,\Lambda_{\mathbf q}}.
$$
The first is <conserved order-parameter dynamics>; its deterministic rate and conserved-noise amplitude vanish at $q=0$. The second is <nonconserved order-parameter dynamics>.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 353 / 3 / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 353 / 3 / i / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 353 / 3 / i / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)