Wide Angle Redshift Distortions Revisited

We explore linear redshift distortions in wide angle surveys from the point of view of symmetries. We show that the redshift space two-point correlation function can be expanded into tripolar spherical harmonics of zero total angular momentum $S_{l_1 l_2 l_3}(\hat x_1, \hat x_2, \hat x)$. The coefficients of the expansion $B_{l_1 l_2 l_3}$ are analogous to the $C_l$'s of the angular power spectrum, and express the anisotropy of the redshift space correlation function. Moreover, only a handful of $B_{l_1 l_2 l_3}$ are non-zero: the resulting formulae reveal a hidden simplicity comparable to distant observer limit. The $B_{l_1 l_2 l_3}$ depend on spherical Bessel moments of the power spectrum and $f = \Omega^{0.6}/b$. In the plane parallel limit, the results of \cite{Kaiser1987} and \cite{Hamilton1993} are recovered. The general formalism is used to derive useful new expressions. We present a particularly simple trigonometric polynomial expansion, which is arguably the most compact expression of wide angle redshift distortions. These formulae are suitable to inversion due to the orthogonality of the basis functions. An alternative Legendre polynomial expansion was obtained as well. This can be shown to be equivalent to the results of \cite{SzalayEtal1998}. The simplicity of the underlying theory will admit similar calculations for higher order statistics as well.Comment: 6 pages, 1 figure, ApJL submitte

Fluctuation properties of laser light after interaction with an atomic system: comparison between two-level and multilevel atomic transitions

The complex internal atomic structure involved in radiative transitions has an effect on the spectrum of fluctuations (noise) of the transmitted light. A degenerate transition has different properties in this respect than a pure two-level transition. We investigate these variations by studying a certain transition between two degenerate atomic levels for different choices of the polarization state of the driving laser. For circular polarization, corresponding to the textbook two-level atom case, the optical spectrum shows the characteristic Mollow triplet for strong laser drive, while the corresponding noise spectrum exhibits squeezing in some frequency ranges. For a linearly polarized drive, corresponding to the case of a multilevel system, additional features appear in both optical and noise spectra. These differences are more pronounced in the regime of a weakly driven transition: whereas the two-level case essentially exhibits elastic scattering, the multilevel case has extra noise terms related to spontaneous Raman transitions. We also discuss the possibility to experimentally observe these predicted differences for the commonly encountered case where the laser drive has excess noise in its phase quadrature.Comment: New version. Accepted for publication in Physical Review

Incoherent multi-gap optical solitons in nonlinear photonic lattices

We demonstrate numerically that partially incoherent light can be trapped in the spectral band gaps of a photonic lattice, creating partially incoherent multi-component spatial optical solitons in a self-defocusing nonlinear periodic medium. We find numerically such incoherent multi-gap optical solitons and discuss how to generate them in experiment by interfering incoherent light beams at the input of a nonlinear periodic medium.Comment: 9 pages, 5 figure

Can We Detect the Anisotropic Shapes of Quasar HII Regions During Reionization Through The Small-Scale Redshifted 21cm Power Spectrum?

Light travel time delays distort the apparent shapes of HII regions surrounding bright quasars during early stages of cosmic reionization. Individual HII regions may remain undetectable in forthcoming redshifted 21 cm experiments. However, the systematic deformation along the line of sight may be detectable statistically, either by stacking tomographic 21cm images of quasars identified, for example, by JWST, or as small-scale anisotropy in the three-dimensional 21cm power spectrum. Here we consider the detectability of this effect. The anisotropy is largest when HII regions are large and expand rapidly, and we find that if bright quasars contributed to the early stages of reionization, then they can produce significant anisotropy, on scales comparable to the typical sizes of HII regions of the bright quasars (approx. 30 Mpc and below). The effect therefore cannot be ignored when analyzing future 21cm power spectra on small scales. If 10 percent of the volume of the IGM at redshift z=10 is ionized by quasars with typical ionizing luminosity of S= 5 x 10^{56} photons/second, the distortions can enhance by more than 10 percent the 21cm power spectrum in the radial (redshift) direction, relative to the transverse directions. The level of this anisotropy exceeds that due to redshift-space distortion, and has the opposite sign. We show that on-going experiments such as MWA should be able to detect this effect. A detection would reveal the presence of bright quasars, and shed light on the ionizing yield and age of the ionizing sources, and the distribution and small-scale clumping of neutral intergalactic gas in their vicinity.Comment: Version accepted by ApJ, with new fiducial model and improved discussio

A wave-envelope of sound propagation in nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave, thereby reducing the computation time and the round-off error encountered in purely numerical techniques. The solution recovers the solution based on the method of multiple scales for slowly varying duct geometry. A computer program was developed based on the wave-envelope analysis for general mean flows. Results are presented for the reflection and transmission coefficients as well as the acoustic pressure distributions for a number of conditions: both straight and variable area ducts with and without liners and mean flows from very low to high subsonic speeds are considered

Effective Fokker-Planck Equation for Birhythmic Modified van der Pol Oscillator

We present an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation associated with the Langevin equation of the birhythmic modified van der Pol system. The solution enables us to derive probability distributions analytically as well as the activation energies associated to switching between the coexisting different attractors that characterize the birhythmic system. Comparing analytical and numerical results we find good agreement when the frequencies of both attractors are equal, while the predictions of the analytic estimates deteriorate when the two frequencies depart. Under the effect of noise the two states that characterize the birhythmic system can merge, inasmuch as the parameter plane of the birhythmic solutions is found to shrink when the noise intensity increases. The solution of the Fokker-Planck equation shows that in the birhythmic region, the two attractors are characterized by very different probabilities of finding the system in such a state. The probability becomes comparable only for a narrow range of the control parameters, thus the two limit cycles have properties in close analogy with the thermodynamic phases

Transmission of sound through nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined, circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. Although the theory is described for circular ducts, it is applicable to other duct configurations - annular, two dimensional, and rectangular. The theory is described for the linear problem, but the technique is general and has the advantage of being applicable to the nonlinear case as well as the linear case. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave. A computer program was developed. The mean flow model consists of a one dimensional flow in the core and a quarter-sine profile in the boundary layer. Results are presented for the reflection and transmission coefficients in ducts with varying slopes and carrying different mean flows

Cosmological redshift distortion: deceleration, bias and density parameters from future redshift surveys of galaxies

The observed two-point correlation functions of galaxies in redshift space become anisotropic due to the geometry of the universe as well as due to the presence of the peculiar velocity field. On the basis of linear perturbation theory, we expand the induced anisotropies of the correlation functions with respect to the redshift $z$, and obtain analytic formulae to infer the deceleration parameter $q_0$, the density parameter $\Omega_0$ and the derivative of the bias parameter $d\ln b/dz$ at $z=0$ in terms of the observable statistical quantities. The present method does not require any assumption of the shape and amplitude of the underlying fluctuation spectrum, and thus can be applied to future redshift surveys of galaxies including the Sloan Digital Sky Survey. We also evaluate quantitatively the systematic error in estimating the value of $\beta_0 \equiv \Omega_0^{0.6}/b$ from a galaxy redshift survey on the basis of a conventional estimator for $\beta_0$ which neglects both the geometrical distortion effect and the time evolution of the parameter $\beta(z)$. If the magnitude limit of the survey is as faint as 18.5 (in B-band) as in the case of the Sloan Digital Sky Survey, the systematic error ranges between -20% and 10% depending on the cosmological parameters. Although such systematic errors are smaller than the statistical errors in the current surveys, they will dominate the expected statistical error for future surveys.Comment: 9 pages, 5 figs, aastex, ApJ in press, replaced version includes minor correction