10,817 research outputs found
Weakly Nonlinear Density-Velocity Relation
We rigorously derive weakly nonlinear relation between cosmic density and
velocity fields up to third order in perturbation theory. The density field is
described by the mass density contrast, \de. The velocity field is described
by the variable \te proportional to the velocity divergence, \te = -
f(\Omega)^{-1} H_0^{-1} \nabla\cdot\bfv, where , is the cosmological density parameter and is the
Hubble constant. Our calculations show that mean \de given \te is a third
order polynomial in \te, \lan \de \ran|_{\te} = a_1 \te + a_2 (\te^2 -
\s_\te^2) + a_3 \te^3. This result constitutes an extension of the formula
\lan \de \ran|_{\te} = \te + a_2 (\te^2 - \s_\te^2), found by
Bernardeau~(1992) which involved second order perturbative solutions. Third
order perturbative corrections introduce the cubic term. They also, however,
cause the coefficient to depart from unity, in contrast with the linear
theory prediction. We compute the values of the coefficients for
scale-free power spectra, as well as for standard CDM, for Gaussian smoothing.
The coefficients obey a hierarchy , meaning that the
perturbative series converges very fast. Their dependence on is
expected to be very weak. The values of the coefficients for CDM spectrum are
in qualitative agreement with the results of N-body simulations by Ganon et al.
(1996). The results provide a method for breaking the -bias degeneracy
in comparisons of cosmic density and velocity fields such as IRAS-POTENT.Comment: 34 pages, figures included, minor changes, a few references added,
accepted for publication in MNRA
Quantum state estimation with unknown measurements
Improved measurement techniques are central to technological development and
foundational scientific exploration. Quantum optics relies upon detectors
sensitive to non-classical features of light, enabling precise tests of
physical laws and quantum-enhanced technologies such as precision measurement
and secure communications. Accurate detector response calibration for
quantum-scale inputs is key to future research and development in these cognate
areas. To address this requirement quantum detector tomography (QDT) has been
recently introduced. However, the QDT approach becomes increasingly challenging
as the complexity of the detector response and input space grows. Here we
present the first experimental implementation of a versatile alternative
characterization technique to address many-outcome quantum detectors by
limiting the input calibration region. To demonstrate the applicability of this
approach the calibrated detector is subsequently used to estimate non-classical
photon number states.Comment: 7 pages, 3 figure
- …