We introduce a formalism for calculating dynamic response functions using experimental single particle Greens functions derived from angle resolved photoemission spectroscopy (ARPES). As an illustration of this procedure we estimate the dynamic spin response of the cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$. We find good agreement with superconducting state neutron data, in particular the $(pi,pi)$ resonance with its unusual `reversed magnon dispersion. We anticipate our formalism will also be of useful in interpreting results from other spectroscopies, such as optical and Raman responses.
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