Raising and Lowering operators of spin-weighted spheroidal harmonics

In this paper we generalize the spin-raising and lowering operators of spin-weighted spherical harmonics to linear-in-$\gamma$ spin-weighted spheroidal harmonics where $\gamma$ is an additional parameter present in the second order ordinary differential equation governing these harmonics. One can then generalize these operators to higher powers in $\gamma$. Constructing these operators required calculating the $\ell$-, $s$- and $m$-raising and lowering operators (and various combinations of them) of spin-weighted spherical harmonics which have been calculated and shown explicitly in this paper

Interferometric detection of spin-polarized transport in the depletion layer of a metal-GaAs Schottky barrier

It is shown that the Kerr rotation of spin-polarized electrons is modulated by the distance of the electrons from the sample surface. Time-resolved Kerr rotation of optically-excited spin-polarized electrons in the depletion layer of n-doped GaAs displays fast oscillations that originate from an interference between the light reflected from the semiconductor surface and from the front of the electron distribution moving into the semiconductor. Using this effect, the dynamics of the photogenerated charge carriers in the depletion layer of the biased Schottky barrier is measured.Comment: 10 pages, 4 figure

Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation

We present a novel analytic extraction of high-order post-Newtonian (pN) parameters that govern quasi-circular binary systems. Coefficients in the pN expansion of the energy of a binary system can be found from corresponding coefficients in an extreme-mass-ratio inspiral (EMRI) computation of the change $\Delta U$ in the redshift factor of a circular orbit at fixed angular velocity. Remarkably, by computing this essentially gauge-invariant quantity to accuracy greater than one part in $10^{225}$, and by assuming that a subset of pN coefficients are rational numbers or products of $\pi$ and a rational, we obtain the exact analytic coefficients. We find the previously unexpected result that the post-Newtonian expansion of $\Delta U$ (and of the change $\Delta\Omega$ in the angular velocity at fixed redshift factor) have conservative terms at half-integral pN order beginning with a 5.5 pN term. This implies the existence of a corresponding 5.5 pN term in the expansion of the energy of a binary system. Coefficients in the pN series that do not belong to the subset just described are obtained to accuracy better than 1 part in $10^{265-23n}$ at $n$th pN order. We work in a radiation gauge, finding the radiative part of the metric perturbation from the gauge-invariant Weyl scalar $\psi_0$ via a Hertz potential. We use mode-sum renormalization, and find high-order renormalization coefficients by matching a series in $L=\ell+1/2$ to the large-$L$ behavior of the expression for $\Delta U$. The non-radiative parts of the perturbed metric associated with changes in mass and angular momentum are calculated in the Schwarzschild gauge