A topological realization of the congruence subgroup Kernel A

A number of years ago, Kumar Murty pointed out to me that the computation of the fundamental group of a Hilbert modular surface ([7],IV,${\S}$6), and the computation of the congruence subgroup kernel of SL(2) ([6]) were surprisingly similar. We puzzled over this, in particular over the role of elementary matrices in both computations. We formulated a very general result on the fundamental group of a Satake compactification of a locally symmetric space. This lead to our joint paper [1] with Lizhen Ji and Les Saper on these fundamental groups. Although the results in it were intriguingly similar to the corresponding calculations of the congruence subgroup kernel of the underlying algebraic group in [5], we were not able to demonstrate a direct connection (cf. [1], ${\S}$7). The purpose of this note is to explain such a connection. A covering space is constructed from inverse limits of reductive Borel-Serre compactifications. The congruence subgroup kernel then appears as the group of deck transformations of this covering. The key to this is the computation of the fundamental group in [1]

Continuous monitoring can improve indistinguishability of a single-photon source

A new engineering technique using continuous quantum measurement in conjunction with feed-forward is proposed to improve indistinguishability of a single-photon source. The technique involves continuous monitoring of the state of the emitter, processing the noisy output signal with a simple linear estimation algorithm, and feed forward to control a variable delay at the output. In the weak coupling regime, the information gained by monitoring the state of the emitter is used to reduce the time uncertainty inherent in photon emission from the source, which improves the indistinguishability of the emitted photons.Comment: 4 pages, 4 figure

Phase behavior of two-component lipid membranes: theory and experiments

The structure of the ripple phase of phospholipid membranes remains poorly understood in spite of a large number of theoretical studies, with many experimentally established structural features of this phase unaccounted for. In this article we present a phenomenological theory of phase transitions in single- and two-component achiral lipid membranes in terms of two coupled order parameters -- a scalar order parameter describing {\it lipid chain melting}, and a vector order parameter describing the {\it tilt of the hydrocarbon chains} below the chain-melting transition. This model reproduces all the salient structural features of the ripple phase, providing a unified description of the phase diagram and microstructure. In addition, it predicts a variant of this phase which does not seem to have been experimentally observed. Using this model we have calculated generic phase diagrams of two-component membranes. We have also determined the phase diagram of a two-component lipid membrane from x-ray diffraction studies on aligned multilayers. This phase diagram is found to be in good agreement with that calculated from the model.Comment: 10 pages, 10 figure

Bayesian sensitivity analysis of incomplete data: bridging pattern‐mixture and selection models

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109600/1/sim6302.pd

SARAS: a precision system for measurement of the Cosmic Radio Background and signatures from the Epoch of Reionization

SARAS is a correlation spectrometer purpose designed for precision measurements of the cosmic radio background and faint features in the sky spectrum at long wavelengths that arise from redshifted 21-cm from gas in the reionization epoch. SARAS operates in the octave band 87.5-175 MHz. We present herein the system design arguing for a complex correlation spectrometer concept. The SARAS design concept provides a differential measurement between the antenna temperature and that of an internal reference termination, with measurements in switched system states allowing for cancellation of additive contaminants from a large part of the signal flow path including the digital spectrometer. A switched noise injection scheme provides absolute spectral calibration. Additionally, we argue for an electrically small frequency-independent antenna over an absorber ground. Various critical design features that aid in avoidance of systematics and in providing calibration products for the parametrization of other unavoidable systematics are described and the rationale discussed. The signal flow and processing is analyzed and the response to noise temperatures of the antenna, reference termination and amplifiers is computed. Multi-path propagation arising from internal reflections are considered in the analysis, which includes a harmonic series of internal reflections. We opine that the SARAS design concept is advantageous for precision measurement of the absolute cosmic radio background spectrum; therefore, the design features and analysis methods presented here are expected to serve as a basis for implementations tailored to measurements of a multiplicity of features in the background sky at long wavelengths, which may arise from events in the dark ages and subsequent reionization era.Comment: 49 pages, 17 figure

Theory of the asymmetric ripple phase in achiral lipid membranes

We present a phenomenological theory of phase transitions in achiral lipid membranes in terms of two coupled order parameters -- a scalar order parameter describing lipid chain melting, and a vector order parameter describing the tilt of the hydrocarbon chains below the chain-melting transition. Existing theoretical models fail to account for all the observed features of the phase diagram, in particular the detailed microstructure of the asymmetric ripple phase lying between the fluid and the tilted gel phase. In contrast, our two-component theory reproduces all the salient structural features of the ripple phase, providing a unified description of the phase diagram and microstructure

Mass Calibration of Optically Selected DES Clusters Using a Measurement of CMB-cluster Lensing with SPTpol Data

We use cosmic microwave background (CMB) temperature maps from the 500 deg2 SPTpol survey to measure the stacked lensing convergence of galaxy clusters from the Dark Energy Survey (DES) Year-3 redMaPPer (RM) cluster catalog. The lensing signal is extracted through a modified quadratic estimator designed to be unbiased by the thermal Sunyaev–Zel'dovich (tSZ) effect. The modified estimator uses a tSZ-free map, constructed from the SPTpol 95 and 150 GHz data sets, to estimate the background CMB gradient. For lensing reconstruction, we employ two versions of the RM catalog: a flux-limited sample containing 4003 clusters and a volume-limited sample with 1741 clusters. We detect lensing at a significance of 8.7σ(6.7σ) with the flux (volume)–limited sample. By modeling the reconstructed convergence using the Navarro–Frenk–White profile, we find the average lensing masses to be M_(200 m) = (1.62^(+0.32)_(-0.25) [stat.] ± 0.04 [sys.]) and (1.28^(+0.14)_(-0.18) [stat.] ± 0.03 [sys.] x 10^(14) M⊙ for the volume- and flux-limited samples, respectively. The systematic error budget is much smaller than the statistical uncertainty and is dominated by the uncertainties in the RM cluster centroids. We use the volume-limited sample to calibrate the normalization of the mass-richness scaling relation, and find a result consistent with the galaxy weak-lensing measurements from DES

Gaussian approximation and single-spin measurement in OSCAR MRFM with spin noise

A promising technique for measuring single electron spins is magnetic resonance force microscopy (MRFM), in which a microcantilever with a permanent magnetic tip is resonantly driven by a single oscillating spin. If the quality factor of the cantilever is high enough, this signal will be amplified over time to the point that it can be detected by optical or other techniques. An important requirement, however, is that this measurement process occur on a time scale short compared to any noise which disturbs the orientation of the measured spin. We describe a model of spin noise for the MRFM system, and show how this noise is transformed to become time-dependent in going to the usual rotating frame. We simplify the description of the cantilever-spin system by approximating the cantilever wavefunction as a Gaussian wavepacket, and show that the resulting approximation closely matches the full quantum behavior. We then examine the problem of detecting the signal for a cantilever with thermal noise and spin with spin noise, deriving a condition for this to be a useful measurement.Comment: 12 pages, 8 figures in EPS format, RevTeX 4.