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\dot{\mathbf m}=\mathbf\Omega(t)\times\mathbf m,\quad \Omega_x(t)=A e^{-(t-t_0)^2/(2\sigma^2)},

\rho_\theta=\frac{1}{2}\left(I+\mathbf r_\theta\cdot\boldsymbol\sigma\right),

F_Q(\theta)=\left|\partial_\theta\mathbf r\right|^2 +\frac{\left(\mathbf r\cdot\partial_\theta\mathbf r\right)^2}{1-\left|\mathbf r\right|^2},

\partial_{\gamma_\phi}\mathbf r(t)\approx \frac{\mathbf r(t;\gamma_\phi+\delta\gamma)-\mathbf r(t;\gamma_\phi)}{\delta\gamma}.

\tilde F_Q(t)=Q_{\gamma_\phi}(t)=\gamma_\phi^2 F_Q(t),

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