On the Search for Quasar Light Echoes

The UV radiation from a quasar leaves a characteristic pattern in the distribution of ionized hydrogen throughout the surrounding space. This pattern or light echo propagates through the intergalactic medium at the speed of light, and can be observed by its imprint on the Ly-alpha forest spectra of background sources. As the echo persists after the quasar has switched off, it offers the possibility of searching for dead quasars, and constraining their luminosities and lifetimes. We outline a technique to search for and characterize these light echoes. To test the method, we create artificial Ly-alpha forest spectra from cosmological simulations at z=3, apply light echoes and search for them. We show how the simulations can also be used to quantify the significance level of any detection. We find that light echoes from the brightest quasars could be found in observational data. With absorption line spectra of 100 redshift z~3-3.5 quasars or galaxies in a 1 square degree area, we expect that ~10 echoes from quasars with B band luminosities L_B=3x10^45 ergs/s exist that could be found at 95% confidence, assuming a quasar lifetime of ~10^7 yr. Even a null result from such a search would have interesting implications for our understanding of quasar luminosities and lifetimes.Comment: 9 pages, 7 figures, ApJ in pres

Affine equivariant rank-weighted L-estimation of multivariate location

In the multivariate one-sample location model, we propose a class of flexible robust, affine-equivariant L-estimators of location, for distributions invoking affine-invariance of Mahalanobis distances of individual observations. An involved iteration process for their computation is numerically illustrated.Comment: 16 pages, 4 figures, 6 table

Keldysh Nonlinear Sigma Model for a Free-Fermion Gas under Continuous Measurements

We analytically analyze the quantum dynamics of a $d$-dimension free-fermion gas subject to continuous projective measurements. By mapping the Lindblad master equation to the functional Keldysh field theory, we observe that the Keldysh Lindblad partition function resembles that in the Keldysh treatment of the disordered fermionic systems. Based on this observation, we develop an effective theory termed as the Keldysh nonlinear sigma model to describe the low-energy physics. Two types of diffuson correlators, similar to those in the disordered fermionic systems, are derived. In addition, up to the one-loop level of the effective theory, we obtain a Drude-form conductivity where the elastic scattering time is replaced by the inverse measurement strength. According to these similarities, these two different concepts, i.e., projective measurements and disorders, are unified in the same framework.Comment: 10 pages, updated the reference list in V