Generalized Reaction Operator

Available identifiers

MaRDI QIDQ6775376

generalized version of the reaction operator

Defining Formula: $\begin{array}{rl}\widetilde{{ℛ}}f(\mathbf{𝐧},\mathbf{𝐦}):\equiv & k_1\{f({{𝒪}}_1^{-}\mathbf{𝐧},\mathbf{𝐦})-f(\mathbf{𝐧},\mathbf{𝐦})\}\\ & +\frac{k_2}{\gamma }\sum _{j=1}^{K_A}\sum _{i\in {ℐ}(j)}\{(n_j+1)f({{𝒪}}_j^{+}\mathbf{𝐧},{{𝒪}}_i^{-}\mathbf{𝐦})-n_{j}f(\mathbf{𝐧},\mathbf{𝐦})\}\\ & +k_3\sum _{i=1}^{K_B}\{(m_i+1)f(\mathbf{𝐧},{{𝒪}}_i^{+}\mathbf{𝐦})-m_{i}f(\mathbf{𝐧},\mathbf{𝐦})\}.\end{array}$

${{𝒪}}_i^{+}$ symbol represents Operators Oi Plus

${{𝒪}}_i^{-}$ symbol represents Operators Oi Minus

$p(\mathbb{(}n),\mathbb{(}m),t)$ symbol represents Joint Probability

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Quantities specializing Generalized Reaction Operator

Reaction Operator

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