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cailixun
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add sec_cutoff info and warning
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docs/src/users_guide/time_evolution/brmesolve.md

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@@ -55,7 +55,7 @@ In the eigenbasis of the system Hamiltonian, where ``A_{mn}(t) = A_{mn} e^{i\ome
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```math
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\begin{aligned}
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\frac{d}{dt} \rho_{ab}(t) = & -i\omega_{ab}\rho_{ab}(t)\\
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&-\hbar^{-2} \sum_{\alpha,\beta} \sum_{c,d}^{\rm sec} \int_0^\infty d\tau\;
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&-\hbar^{-2} \sum_{\alpha,\beta} \sum_{c,d}^{\textrm{sec}} \int_0^\infty d\tau\;
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\left\{
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g_{\alpha\beta}(\tau)
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\left[\delta_{bd}\sum_nA^\alpha_{an}A^\beta_{nc}e^{i\omega_{cn}\tau}
@@ -87,7 +87,7 @@ where ``\lambda_{ab}(\omega)`` is an energy shift that is neglected here. The fi
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=
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-i\omega_{ab}\rho_{ab}(t)
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+
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\sum_{c,d}^{\rm sec}R_{abcd}\rho_{cd}(t),
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\sum_{c,d}^{\textrm{sec}}R_{abcd}\rho_{cd}(t),
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```
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where
@@ -213,3 +213,17 @@ sol = brmesolve(H, ψ0, tlist, ((sigmax(),ohmic_spectrum),); e_ops=e_ops)
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```
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The resulting `sol` is of the `struct` [`TimeEvolutionSol`](@ref) as [`mesolve`](@ref).
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!!! note "Secular cutoff"
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While the code example simulates the Bloch-Redfield equation in the secular approximation, `QuantumToolbox`'s implementation allows the user to simulate the non-secular version of the Bloch-Redfield equation by setting `sec_cutoff=-1`, as well as do a partial secular approximation by setting it to a `Float64` , this float number will become the cutoff for the summation (``\sum_{c,d}^{\textrm{sec}}``) in the previous equations, meaning that terms with ``\omega_{ab} - \omega_{cd}`` greater than the `sec_cutoff` will be neglected. Its default value is `0.1` which corresponds to the secular approximation.
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For example, the command
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```julia
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sol = brmesolve(H, ψ0, tlist, ((sigmax(),ohmic_spectrum),); e_ops=e_ops, sec_cutoff=-1)
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```
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will simulate the same example as above without the secular approximation.
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!!! warning "Secular cutoff"
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Using the non-secular version may lead to negativity issues.

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