Anomalous Spin and Charge Dynamics of thet-JModel at Low Doping

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