From 2a722a95e750ae41cdc366e38590169f50347959 Mon Sep 17 00:00:00 2001 From: Federico Cerisola Date: Mon, 19 Aug 2024 22:00:43 +0100 Subject: [PATCH] Fix typos in docs --- docs/src/units.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/docs/src/units.md b/docs/src/units.md index c72c472..3950d6a 100644 --- a/docs/src/units.md +++ b/docs/src/units.md @@ -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