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Fix typos in docs
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cerisola committed Aug 19, 2024
1 parent 2f1ccf4 commit 2a722a9
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions docs/src/units.md
Original file line number Diff line number Diff line change
@@ -14,12 +14,12 @@ for a single spin ``\mathbf{S}`` in presence of an external field
``\mathbf{B}_\mathrm{ext}`` read
```math
\frac{\mathrm{d}\mathbf{S}}{\mathrm{d}t} =
\gamma\mathbf{S}\times\left(\mathbf{B}_\mathrm{ext} + \mathbf{b}(t) + \mathbf{V}(t)\right),
\gamma_e\mathbf{S}\times\left(\mathbf{B}_\mathrm{ext} + \mathbf{b}(t) + \mathbf{V}(t)\right),
```
where $\gamma_e$ is the electron gyromagnetic ratio, ``b(t)`` is the environment
induced thermal stochastic field, and
```math
\mathbf{V}(t) = \gamma \int_{-\infty}^{t}\mathrm{d}t' \, \mathbf{K}(t-t')\mathbf{S}(t'),
\mathbf{V}(t) = \gamma_e\int_{-\infty}^{t}\mathrm{d}t' \, \mathbf{K}(t-t')\mathbf{S}(t'),
```
where ``\mathbf{K}(\tau)`` is a memory kernel accounting for the non-Markovian
evolution of the spin (see [NJP 24 033020 (2022)](https://www.doi.org/10.1088/1367-2630/ac4ef2)
@@ -28,9 +28,9 @@ SpiDy focuses on the case of an environment with a Lorentzian spectral density,
in which case these equations of motion can be rewritten as
```math
\frac{\mathrm{d}\mathbf{S}}{\mathrm{d}t} =
\gamma\mathbf{S}\times\left(\mathbf{B}_\mathrm{ext} + \mathbf{b} + \mathbf{V}\right), \\
\gamma_e\mathbf{S}\times\left(\mathbf{B}_\mathrm{ext} + \mathbf{b} + \mathbf{V}\right), \\
\frac{\mathrm{d}\mathbf{V}}{\mathrm{d}t} = \mathbf{W}, \\
\frac{\mathrm{d}\mathbf{W}}{\mathrm{d}t} = \gamma A \mathbf{S} - \omega_0^2\mathbf{V} - \Gamma\mathbf{W},
\frac{\mathrm{d}\mathbf{W}}{\mathrm{d}t} = \gamma_e A \mathbf{S} - \omega_0^2\mathbf{V} - \Gamma\mathbf{W},
```
where ``A``, ``\omega_0``, and ``\Gamma`` parametrise the Lorentzian spectral density as
```math

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