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I don't know the specific context that you may be looking for, but it's quite common to use a four-point correlation function of the quantum dipole moment operator to retrieve non-linear relaxation dynamics. These correlation functions make up the nonlinear response function of a material system to an electric field which, when convolved with the excitation ...

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I found it very difficult to understand your question, but here is an attempt at answering it: The whole point of embedding is to uncover the phase-space structure or, with other words, something that is topologically equivalent to the attractor. For any interesting system, this is not describable by your usual distributions (and also it is usually not ...

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There is something you should be careful of regarding Liouville's theorem. If there are momentum-dependent forces, then Liouville's theorem changes because phase density is no longer incompressible. Suppose we define $f_{s}$ = $f_{s}(\mathbf{x},\mathbf{p},t)$ $\equiv$ the particle distribution function of species $s$, which is non-negative, contains a ...

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