Anomalous spin and charge dynamics of the t-J model at low doping.

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We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of 2D $t\ensuremath{-}J$ model for hole dopings $\ensuremath{\le}25$%. Both correlation functions show a remarkably regular, but very different, scaling with both hole density ${\ensuremath{\rho}}_{h}$ and parameters $t$ and $J$. The density correlation function is most consistent with that of condensed bosons in a band of width $\ensuremath{\sim}t$, the spin correlation function with that of fermions in a band of width $\ensuremath{\sim}J$. We show that the familiar spin bag scenario explains these results in a natural way.