1,440 research outputs found
Demodulation of intensity and shot noise in the optical heterodyne detection of laser interferometers for gravitational waves
Demodulation of intensity noise in the optical heterodyne detector is analyzed for application in interferometric gravitational-wave detectors. The correlation function and the power spectral density of the demodulated intensity noise are derived, taking into account the effect of bandpass filtering at the photodiode and an arbitrary demodulation waveform. The analysis includes demodulation of the rf-modulated shot noise as a special case of the intensity noise. For shot-noise-limited detection, the signal-to-noise ratio is found as a function of the modulation parameters, and the optimization of the signal-to-noise ratio with respect to the demodulation phase is described
Fermi-normal, optical, and wave-synchronous coordinates for spacetime with a plane gravitational wave
Fermi normal coordinates provide a standardized way to describe the effects
of gravitation from the point of view of an inertial observer. These
coordinates have always been introduced via perturbation expansions and were
usually limited to distances much less than the characteristic length scale set
by the curvature of spacetime. For a plane gravitational wave this scale is
given by its wavelength which defines the domain of validity for these
coordinates known as the long-wavelength regime. The symmetry of this
spacetime, however, allows us to extend Fermi normal coordinates far beyond the
long-wavelength regime. Here we present an explicit construction for this
long-range Fermi normal coordinate system based on the unique solution of the
boundary-value problem for spacelike geodesics. The resulting formulae amount
to summation of the infinite series for Fermi normal coordinates previously
obtained with perturbation expansions. We also consider two closely related
normal coordinate systems: optical coordinates which are built from null
geodesics and wave-synchronous coordinates which are built from spacelike
geodesics locked in phase with the propagating gravitational wave. The
wave-synchronous coordinates yield the exact solution of Peres and Ehlers-Kundt
which is globally defined. In this case, the limitation of the long-wavelength
regime is completely overcome, and the system of wave-synchronous coordinates
becomes valid for arbitrarily large distances. Comparison of the different
coordinate systems is done by considering the motion of an inertial test mass
in the field of a plane gravitational wave
Transfer Functions for Fields in a 3-mirror Nested Cavity
Transfer functions for the fields in a 3-mirror nested cavity are obtained. Explicit formulas for their poles and zeros are found. These results are used for simple analysis of the response of power recycling and signal recycling interferometers
Evaluation of the two-particle propagator for Hubbard model with the help of Hubbard-I approximation
The Hubbard-I approximation is generalized to allow for direct evaluation of
the equal-time anomalous two-electron propagator for Hubbard model on
two-dimensional square lattice. This propagator is compared against the quantum
Monte Carlo data obtained by Aimi and Imada [J. Phys. Soc. Jpn. {\bf 76},
113708 (2007)] in the limit of strong electron-electron interaction. The
Hubbard-I predictions are in a good qualitative agreement with the Monte Carlo
results. In particular, -wave correlations decay as ("free
electron" behaviour), if separation exceeds 2-3 lattice constants. However,
the Hubbard-I approximation underestimates coefficient by a factor of about
three. We conclude that the Hubbard-I approximation, despite its simplicity and
artefacts, captures the qualitative behaviour of the two-particle propagator
for the Hubbard model, at least for moderate values of .Comment: 17 pages, 5 figures; the text is reorganized somewhat as compared to
the preprint's previous version; an extra figure is added; some figures are
re-drawn for different parameter values; typeset with IOP styl
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