Spin dynamics of SrCu$_2$O$_3$ and the Heisenberg ladder

The $S=1/2$ Heisenberg antiferromagnet in the ladder geometry is studied as a model for the spin degrees of freedom of SrCu$_2$O$_3$. The susceptibility and the spin echo decay rate are calculated using a quantum Monte Carlo technique, and the spin-lattice relaxation rate is obtained by maximum entropy analytic continuation of imaginary time correlation functions. All calculated quantities are in reasonable agreement with experimental results for SrCu$_2$O$_3$ if the exchange coupling $J \approx 850$K, i.e. significantly smaller than in high-T$_c$ cuprates.