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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2023

Paper 209

The field leaves rotations fixing its unit direction $e$ as symmetries. Consequently the expectation vector is parallel to $e$:
$$
\lim_{h\downarrow0}\lim_{L\to\infty}\langle\sigma_0\rangle_{\Lambda_L,\beta,h}
=m e.
$$
For any $u\in\mathbb R^n$, linearity therefore gives
$$
\lim_{h\downarrow0}\lim_{L\to\infty}
\langle\sigma_0\cdot u\rangle_{\Lambda_L,\beta,h}
=m(e\cdot u).
$$


Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 209 / 2 / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 209 / 2 / iii / Solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 209 / 2 / iii / Solution

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