How can I apply the energy dissipation form of the Spin-Boson model to both time-dependent and time-independent cases in my code?

[nelyasi]

I am wondering about the exact approach to use the energy dissipation form of the Spin-Boson model, as described in the tutorial, for both time-dependent and time-independent forms. Specifically, in the interaction Hamiltonian, instead of considering the system operator as ( \sigma_z ), I want to use the raising and lowering operators ( \sigma_+ ) and ( \sigma_- ), such that:

[
H_{I} = \frac{1}{2}\sum_{k}g_{k}(\sigma_{-}a^{\dag} + \text{hc})
]

Can I write the code like this?

sigma_p = oqupy.operators.sigma("+")
bath = oqupy.Bath(0.5 * sigma_p, correlations)