5,740 research outputs found
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
The transformative forces of international law? Questioning equality regimes from a multi-level perspective
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
- …