Nakajima-Zwanzig-Gleichung

Nakajima Zwanzig Equation Fehler beim Parsen (Unbekannte Funktion „\math“): {\displaystyle \begin{align} & {{d}_{t}}\chi =L\chi \\ & \chi =\mathcal{P}\chi +\mathcal{Q}\chi \end{align} <\math><math> \begin{align} & {{d}_{t}}\left( \begin{matrix} \mathcal{P} \\ \mathcal{Q} \\ \end{matrix} \right)\chi =\left( \begin{matrix} \mathcal{P} \\ \mathcal{Q} \\ \end{matrix} \right)L\left( \begin{matrix} \mathcal{P} \\ \mathcal{Q} \\ \end{matrix} \right)\chi +\left( \begin{matrix} \mathcal{P} \\ \mathcal{Q} \\ \end{matrix} \right)L\left( \begin{matrix} \mathcal{Q} \\ \mathcal{P} \\ \end{matrix} \right)\chi \\ & \Rightarrow \mathcal{Q}\chi ={{e}^{\mathcal{Q}Lt}}Q{{\chi }_{0}}+\int '{{e}^{\mathcal{Q}Lt}}\mathcal{Q}L\mathcal{P}\chi (t-{t}') \\ & \Rightarrow {{\text{d}}_{t}}\mathcal{P}\chi =\mathcal{P}L\mathcal{P}\chi +\underbrace{\mathcal{P}{{e}^{\mathcal{Q}Lt}}Q{{\chi }_{0}}}_{=0}+\mathcal{P}L\int '{{e}^{\mathcal{Q}Lt}}\mathcal{Q}L\mathcal{P}\chi (t-{t}') \\ \end{align} }