A Genus-3 Topological Recursion Relation

In this paper, we give a new genus-3 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds. This formula also applies to intersection numbers on moduli spaces of spin curves. A by-product of the proof of this formula is a new relation in the tautological ring of the moduli space of 1-pointed genus-3 stable curves.Comment: Final version. To appear in Commmunications of Mathematical Physics. Corrected some typos and added a section on intersection numbers on moduli spaces of curves. LaTex file, 19 pages, 1 figur

Evolution of the spin Hall effect in Pt nanowires: Size and temperature effects

We have studied the evolution of the Spin Hall Effect in the regime where the material size responsible for the spin accumulation is either smaller or larger than the spin diffusion length. Lateral spin valve structures with Pt insertions were successfully used to measure the spin absorption efficiency as well as the spin accumulation in Pt induced through the spin Hall effect. Under a constant applied current the results show a decrease of the spin accumulation signal is more pronounced as the Pt thickness exceeds the spin diffusion length. This implies that the spin accumulation originates from bulk scattering inside the Pt wire and the spin diffusion length limits the SHE. We have also analyzed the temperature variation of the spin hall conductivity to identify the dominant scattering mechanism.Comment: 4 pages, 4 figure