Primordial B-mode Diagnostics and Self Calibrating the CMB Polarization

Distortions in the primordial cosmic microwave background (CMB) along the line-of-sight can be modeled and described using 11 fields. These distortion fields correspond to various cosmological signals such as weak gravitational lensing of the CMB by large-scale structure, screening from patchy reionization, rotation of the plane of polarization due to magnetic fields or parity violating physics. Various instrumental systematics such as gain fluctuations, pixel rotation, differential gain, pointing, differential ellipticity are also described by the same distortion model. All these distortions produce B-mode that contaminate the primordial tensor B-modes signal. In this paper we show that apart from generating B-modes, each distortion uniquely couples different modes (\bfl_1\ne \bfl_2) of the CMB anisotropies, generating $$ correlations which for the primordial CMB are zero. We describe and implement unbiased minimum variance quadratic estimators which using the off diagonal correlations in the CMB can extract the map of distortions. We perform Monte-Carlo simulations to characterize the estimators and illustrate the level of distortions that can be detected with current and future experiments. The estimators can be used to look for cosmological signals, or to check for any residual systematics in the data. As a specific example of primordial tensor B-mode diagnostics we compare the level of minimum detectable distortions using our method with maximum allowed distortion level for the B-modes detection. We show that for any experiment, the distortions will be detected at high significance using correlations before they would show up as spurious B-modes in the power spectrum.Comment: 14 pages, 4 figure

Towards Bose-Einstein Condensation of Electron Pairs: Role of Schwinger Bosons

It can be shown that the bosonic degree of freedom of the tightly bound on-site electron pairs could be separated as Schwinger bosons. This is implemented by projecting the whole Hilbert space into the Hilbert subspace spanned by states of two kinds of Schwinger bosons (to be called binon and vacanon) subject to a constraint that these two kinds of bosonic quasiparticles cannot occupy the same site. We argue that a binon is actually a kind of quantum fluctuations of electron pairs, and a vacanon corresponds to a vacant state. These two bosonic quasiparticles may be responsible for the Bose-Einstein condensation (BEC) of the system associated with electron pairs. These concepts are also applied to the attractive Hubbard model with strong coupling, showing that it is quite useful. The relevance of the present arguments to the existing theories associated with the BEC of electron pairs is briefly commented.Comment: Revtex, one figur

Constraining a spatially dependent rotation of the Cosmic Microwave Background Polarization

Following Kamionkowski (2008), a quadratic estimator of the rotation of the plane of polarization of the CMB is constructed. This statistic can estimate a spatially varying rotation angle. We use this estimator to quantify the prospects of detecting such a rotation field with forthcoming experiments. For PLANCK and CMBPol we find that the estimator containing the product of the E and B components of the polarization field is the most sensitive. The variance of this EB estimator, N(L) is roughly independent of the multipole L, and is only weakly dependent on the instrumental beam. For FWHM of the beam size ~ 5'-50', and instrument noise $\Delta_p ~ 5-50 uK-arcmin, the scaling of variance N(L) can be fitted by a power law N(L)=3.3 x 10^{-7} \Delta^2_p (FWHM)^{1.3} sq-deg. For small instrumental noise \Delta_p \leq 5 uK-arcmin, the lensing B-modes become important, saturating the variance to ~10^{-6} sq-deg even for an ideal experiment. Upcoming experiments like PLANCK will be able to detect a power spectrum of the rotation angle, C^{\alpha \alpha}(L), as small as 0.01 sq-deg, while futuristic experiment like CMBPol will be able to detect rotation angle power spectrum as small as 2.5 x 10^{-5} sq-deg. We discuss the implications of such constraints, both for the various physical effects that can rotate the polarization as photons travel from the last scattering surface as well as for constraints on instrumental systematics that can also lead to a spurious rotation signal. Rotation of the CMB polarization generates B-modes which will act as contamination for the primordial B-modes detection. We discuss an application of our estimator to de-rotate the CMB to increase the sensitivity for the primordial B-modes.Comment: 11 pages, 5 figure

Numerical Study of the Correspondence Between the Dissipative and Fixed Energy Abelian Sandpile Models

We consider the Abelian sandpile model (ASM) on the large square lattice with a single dissipative site (sink). Particles are added by one per unit time at random sites and the resulting density of particles is calculated as a function of time. We observe different scenarios of evolution depending on the value of initial uniform density (height) $h_0=0,1,2,3$. During the first stage of the evolution, the density of particles increases linearly. Reaching a critical density $\rho_c(h_0)$, the system changes its behavior sharply and relaxes exponentially to the stationary state of the ASM with $\rho_s=25/8$. We found numerically that $\rho_c(0)=\rho_s$ and $\rho_c(h_0>0) \neq \rho_s$. Our observations suggest that the equality $\rho_c=\rho_s$ holds for more general initial conditions with non-positive heights. In parallel with the ASM, we consider the conservative fixed-energy Abelian sandpile model (FES). The extensive Monte-Carlo simulations for $h_0=0,1,2,3$ have confirmed that in the limit of large lattices $\rho_c(h_0)$ coincides with the threshold density $\rho_{th}(h_0)$ of FES. Therefore, $\rho_{th}(h_0)$ can be identified with $\rho_s$ if the FES starts its evolution with non-positive uniform height $h_0 \leq 0$.Comment: 6 pages, 8 figure

Dynamic Behavior of Precast Concrete Beam-Column Sub-Assemblages with High Performance Connections Subjected to Sudden Column Removal Scenario

Unbonded posttensioned precast concrete (UPPC) structure has shown its excellent aseismic performance in laboratory tests and earthquake investigation. However, the progressive collapse behavior of UPPC subjected to column removal scenario is still unclear. To fill this knowledge gap, two 1/2 scaled UPPC beam-column sub-assemblages were tested under a penultimate column removal scenario. The dynamic test results indicated that UPPC sub-assemblages have desirable load redistribution capacity to mitigate progressive collapse. The failure modes of the sub-assemblages observed in dynamic test were quite similar to that in static counterparts

Mott-Peierls Transition in the extended Peierls-Hubbard model

The one-dimensional extended Peierls-Hubbard model is studied at several band fillings using the density matrix renormalization group method. Results show that the ground state evolves from a Mott-Peierls insulator with a correlation gap at half-filling to a soliton lattice with a small band gap away from half-filling. It is also confirmed that the ground state of the Peierls-Hubbard model undergoes a transition to a metallic state at finite doping. These results show that electronic correlations effects should be taken into account in theoretical studies of doped polyacetylene. They also show that a Mott-Peierls theory could explain the insulator-metal transition observed in this material.Comment: 4 pages with 3 embedded eps figure