Semiclassical Accuracy in Phase Space for Regular and Chaotic Dynamics

A phase-space semiclassical approximation valid to $O(\hbar)$ at short times is used to compare semiclassical accuracy for long-time and stationary observables in chaotic, stable, and mixed systems. Given the same level of semiclassical accuracy for the short time behavior, the squared semiclassical error in the chaotic system grows linearly in time, in contrast with quadratic growth in the classically stable system. In the chaotic system, the relative squared error at the Heisenberg time scales linearly with $\hbar_{\rm eff}$, allowing for unambiguous semiclassical determination of the eigenvalues and wave functions in the high-energy limit, while in the stable case the eigenvalue error always remains of the order of a mean level spacing. For a mixed classical phase space, eigenvalues associated with the chaotic sea can be semiclassically computed with greater accuracy than the ones associated with stable islands.Comment: 9 pages, 6 figures; to appear in Physical Review

Optimizing Outreach and Application Assistance Services in Community-based Organizations: Evaluation Findings from The Colorado Trust's Outreach and Enrollment for Children and Youth Grant Strategy

This report discusses findings from the evaluation of The Colorado Trust's three-year, $3.3 million grant strategy (2009-2011) to help expand enrollment of children and youth in public health insurance programs in Colorado. These findings focus on how 12 community-based organizations, with little previous experience in providing application assistance to families to enroll children and youth in public health insurance, offered targeted outreach and application assistance services. These findings provide new insights into the time, effort and outcomes associated with implementing outreach and application assistance services, reinforcing and expanding upon previous literature demonstrating the promise and potential pitfalls of this approach