Population diffusion and equipartition in quantum systems of many degrees of freedom

In the interaction picture, population transfer among coupled degrees of freedom is greatly enhanced by resonances. We show that statistically the number of resonances increases rapidly with degrees of freedom, changing the characteristic of population transfer from being bounded to diffusive. From the diffusion rate we derive simple expressions for the time scales of energy relaxation and equipartition. These expressions are supported by a wide range of experimental data. The analysis elucidates quantitatively the dependence of equipartition on resonances.