Effective one body Hamiltonian of two spinning black-holes with next-to-next-to-leading order spin-orbit coupling

Building on the recently computed next-to-next-to-leading order (NNLO) post-Newtonian (PN) spin-orbit Hamiltonian for spinning binaries \cite{Hartung:2011te} we extend the effective-one-body (EOB) description of the dynamics of two spinning black-holes to NNLO in the spin-orbit interaction. The calculation that is presented extends to NNLO the next-to-leading order (NLO) spin-orbit Hamiltonian computed in Ref. \cite{Damour:2008qf}. The present EOB Hamiltonian reproduces the spin-orbit coupling through NNLO in the test-particle limit case. In addition, in the case of spins parallel or antiparallel to the orbital angular momentum, when circular orbits exist, we find that the inclusion of NNLO spin-orbit terms moderates the effect of the NLO spin-orbit coupling.Comment: 11 pages, no figures. Corrected typographical errors in Eqs.(43) and (55). Erratum submitted to PR

Diffusion with stochastic resetting at power-law times

What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain {\em exact} closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power-law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for $\alpha < 1$, to one that is time independent for $\alpha > 1$. The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal $\alpha$ that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.Comment: 8 pages, 3 figures. v2: Version published in Phys. Rev. E as a rapid comm., includes Suppl. Ma