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Update theory.md
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tfmlaX authored Apr 15, 2024
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We consider, in the Schrödinger picture, a general Hamiltonian where a non-specified system interacts linearly with a bosonic environments

```math
\hat{H} = \hat{H}_S + \int_0^{+\infty} \hbar\omega\hat{a}^\dagger_\omega\hat{a}_\omega\ \mathrm{d}\omega + \hat{A}_S\int_0^{+\infty}\sqrt{J(\omega)}\left(\hat{a}_\omega + \hat{a}^\dagger_\omega\right)\mathrm{d}\omega
\begin{align}
\hat{H} =& \hat{H}_S + \int_0^{+\infty} \hbar\omega\hat{a}^\dagger_\omega\hat{a}_\omega\ \mathrm{d}\omega + \hat{A}_S\int_0^{+\infty}\sqrt{J(\omega)}\left(\hat{a}_\omega + \hat{a}^\dagger_\omega\right)\mathrm{d}\omega
\end{align}
```


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