Asymptotic channels and gauge transformations of the time-dependent Dirac equation for extremely relativistic heavy-ion collisions

We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit, for the asymptotic channel solutions of the Dirac equation, and elucidate their close connection with gauge transformations which transform the dynamics into a representation in which the interaction between the electron and a distant ion is of short range. We describe the implications of this relationship for solving the time-dependent Dirac equation for extremely relativistic collisions.Comment: 12 pages, RevTeX, 2 figures, submitted to PR

Exact averages of central values of triple product L-functions

We obtain exact formulas for central values of triple product L-functions averaged over newforms of weight 2 and prime level. We apply these formulas to non-vanishing problems. This paper uses a period formula for the triple product L-function proved by Gross and Kudla

Electron Spin Resonance at the Level of 10000 Spins Using Low Impedance Superconducting Resonators

We report on electron spin resonance (ESR) measurements of phosphorus donors localized in a 200 square micron area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design we are able to detect around 20000 spins with a signal-to-noise ratio (SNR) of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1 - 10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Due to the larger coupling rate, we find that spin relaxation is dominated by radiative decay into the resonator and dependent upon the spin-resonator detuning, as predicted by Purcell

Symmetry breaking in a mechanical resonator made from a carbon nanotube

Nanotubes behave as semi-flexible polymers in that they can bend by a sizeable amount. When integrating a nanotube in a mechanical resonator, the bending is expected to break the symmetry of the restoring potential. Here we report on a new detection method that allows us to demonstrate such symmetry breaking. The method probes the motion of the nanotube resonator at nearly zero-frequency; this motion is the low-frequency counterpart of the second overtone of resonantly excited vibrations. We find that symmetry breaking leads to the spectral broadening of mechanical resonances, and to an apparent quality factor that drops below 100 at room temperature. The low quality factor at room temperature is a striking feature of nanotube resonators whose origin has remained elusive for many years. Our results shed light on the role played by symmetry breaking in the mechanics of nanotube resonators.Comment: manuscript and supplementary material, 7 figure

Tail emission from a ring-like jet: its application to shallow decays of early afterglows and to GRB 050709

Similar to the pulsar, the magnetic axis and the spin axis of the gamma-ray burst source may not lie on the same line. This may cause a ring-like jet due to collimation of the precessing magnetic axis. We analyze the tail emission from such a jet, and find that it has a shallow decay phase with temporal index equal to -1/2 if the Lorentz factor of the ejecta is not very high. This phase is consistent with the shallow decay phase of some early X-ray afterglow detected by {\it{swift}}. The ring-like jet has a tail cusp with sharp rising and very sharp decay. This effect can provide an explanation for the re-brightening and sharp decay of the X-ray afterglow of GRB 050709.Comment: 6 pages, 2 figures. Accepted by ChJA