Symmetry protected topological orders of 1D spin systems with D2+T symmetry

In [Z.-X. Liu, M. Liu, X.-G. Wen, arXiv:1101.5680], we studied 8 gapped symmetric quantum phases in S=1 spin chains %/ladders which respect a discrete spin rotation $D_2 \subset SO(3)$ and time reversal $T$ symmetries. In this paper, using a generalized approach, we study all the 16 possible gapped symmetric quantum phases of 1D integer spin systems with only $D_2+T$ symmetry. Those phases are beyond Landau symmetry breaking theory and cannot be characterized by local order parameters, since they do not break any symmetry. They correspond to 16 symmetry protected topological (SPT) orders. We show that all the 16 SPT orders can be fully characterized by the physical properties of the symmetry protected degenerate boundary states (end `spins') at the ends of a chain segment. So we can measure and distinguish all the 16 SPT orders experimentally. We also show that all these SPT orders can be realized in S=1 spin ladder models. The gapped symmetric phases protected by subgroups of $D_2+T$ are also studied. Again, all these phases can be distinguished by physically measuring their end `spins'.Comment: 10+page

Parameter-space metric for all-sky semicoherent searches for gravitational-wave pulsars

The sensitivity of all-sky searches for gravitational-wave pulsars is primarily limited by the finite availability of computing resources. Semicoherent searches are a widely-used method of maximizing sensitivity to gravitational-wave pulsars at fixed computing cost: the data from a gravitational-wave detector are partitioned into a number of segments, each segment is coherently analyzed, and the analysis results from each segment are summed together. The generation of template banks for the coherent analysis of each segment, and for the summation, requires knowledge of the metrics associated with the coherent and semicoherent parameter spaces respectively. We present a useful approximation to the semicoherent parameter-space metric, analogous to that presented in Wette and Prix [Phys. Rev. D 88, 123005 (2013)] for the coherent metric. The new semicoherent metric is compared to previous work in Pletsch [Phys. Rev. D 82, 042002 (2010)], and Brady and Creighton [Phys. Rev. D 61, 082001 (2000)]. We find that semicoherent all-sky searches require orders of magnitude more templates than previously predicted.Comment: 21 pages, 13 figures, 2 table

How does the substrate affect the Raman and excited state spectra of a carbon nanotube?

We study the optical properties of a single, semiconducting single-walled carbon nanotube (CNT) that is partially suspended across a trench and partially supported by a SiO2-substrate. By tuning the laser excitation energy across the E33 excitonic resonance of the suspended CNT segment, the scattering intensities of the principal Raman transitions, the radial breathing mode (RBM), the G-mode and the D-mode show strong resonance enhancement of up to three orders of magnitude. In the supported part of the CNT, despite a loss of Raman scattering intensity of up to two orders of magnitude, we recover the E33 excitonic resonance suffering a substrate-induced red shift of 50 meV. The peak intensity ratio between G-band and D-band is highly sensitive to the presence of the substrate and varies by one order of magnitude, demonstrating the much higher defect density in the supported CNT segments. By comparing the E33 resonance spectra measured by Raman excitation spectroscopy and photoluminescence (PL) excitation spectroscopy in the suspended CNT segment, we observe that the peak energy in the PL excitation spectrum is red-shifted by 40 meV. This shift is associated with the energy difference between the localized exciton dominating the PL excitation spectrum and the free exciton giving rise to the Raman excitation spectrum. High-resolution Raman spectra reveal substrate-induced symmetry breaking, as evidenced by the appearance of additional peaks in the strongly broadened Raman G band. Laser-induced line shifts of RBM and G band measured on the suspended CNT segment are both linear as a function of the laser excitation power. Stokes/anti-Stokes measurements, however, reveal an increase of the G phonon population while the RBM phonon population is rather independent of the laser excitation power.Comment: Revised manuscript, 20 pages, 8 figure

Laser Guide Star for Large Segmented-Aperture Space Telescopes, Part I: Implications for Terrestrial Exoplanet Detection and Observatory Stability

Precision wavefront control on future segmented-aperture space telescopes presents significant challenges, particularly in the context of high-contrast exoplanet direct imaging. We present a new wavefront control architecture that translates the ground-based artificial guide star concept to space with a laser source aboard a second spacecraft, formation flying within the telescope field-of-view. We describe the motivating problem of mirror segment motion and develop wavefront sensing requirements as a function of guide star magnitude and segment motion power spectrum. Several sample cases with different values for transmitter power, pointing jitter, and wavelength are presented to illustrate the advantages and challenges of having a non-stellar-magnitude noise limited wavefront sensor for space telescopes. These notional designs allow increased control authority, potentially relaxing spacecraft stability requirements by two orders of magnitude, and increasing terrestrial exoplanet discovery space by allowing high-contrast observations of stars of arbitrary brightness.Comment: Submitted to A

Phasing the Mirror Segments of the Keck Telescopes: The Broadband Phasing Algorithm

To achieve its full diffraction limit in the infrared, the primary mirror of the Keck telescope (now telescopes) must be properly phased: The steps or piston errors between the individual mirror segments must be reduced to less than 100 nm. We accomplish this with a wave optics variation of the Shack–Hartmann test, in which the signal is not the centroid but rather the degree of coherence of the individual subimages. Using filters with a variety of coherence lengths, we can capture segments with initial piston errors as large as ± 30 µm and reduce these to 30 nm—a dynamic range of 3 orders of magnitude. Segment aberrations contribute substantially to the residual errors of ~75 nm

How a protein searches for its specific site on DNA: the role of intersegment transfer

Proteins are known to locate their specific targets on DNA up to two orders of magnitude faster than predicted by the Smoluchowski three-dimensional diffusion rate. One of the mechanisms proposed to resolve this discrepancy is termed "intersegment transfer". Many proteins have two DNA binding sites and can transfer from one DNA segment to another without dissociation to water. We calculate the target search rate for such proteins in a dense globular DNA, taking into account intersegment transfer working in conjunction with DNA motion and protein sliding along DNA. We show that intersegment transfer plays a very important role in cases where the protein spends most of its time adsorbed on DNA.Comment: 9 pages, 7 figure

AM/FM signal estimation with micro-segmentation and polynomial fit

Cataloged from PDF version of article.Amplitude and phase estimation of AM/FM signals with parametric polynomial representation require the polynomial orders for phase and amplitude to be known. But in reality, they are not known and have to be estimated. A well-known method for estimation is the higher-order ambiguity function (HAF) or its variants. But the HAF method has several reported drawbacks such as error propagation and slowly varying or even constant amplitude assumption. Especially for the long duration time-varying signals like AM/FM signals, which require high orders for the phase and amplitude, computational load is very heavy due to nonlinear optimization involving many variables. This paper utilizes a micro-segmentation approach where the length of segment is selected such that the amplitude and instantaneous frequency (IF) is constant over the segment. With this selection first, the amplitude and phase estimates for each micro-segment are obtained optimally in the LS sense, and then, these estimates are concatenated to obtain the overall amplitude and phase estimates. The initial estimates are not optimal but sufficiently close to the optimal solution for subsequent processing. Therefore, by using the initial estimates, the overall polynomial orders for the amplitude and phase are estimated. Using estimated orders, the initial amplitude and phase functions are fitted to the polynomials to obtain the final signal. The method does not use any multivariable nonlinear optimization and is efficient in the sense that the MSE performance is close enough to the Cramer–Rao bound. Simulation examples are presented