Distinguishing standard reionization from dark matter models

The Wilkinson Microwave Anisotropy Probe (WMAP) experiment has detected reionization at the $5.5 \sigma$ level and has reported a mean optical depth of $0.088 \pm 0.015$. A powerful probe of reionization is the large-angle $EE$ polarization power spectrum, which is now (since the first five years of data from WMAP) cosmic variance limited for $2\le l \le6$. Here we consider partial reionization caused by WIMP dark matter annihilation, and calculate the expected polarization power spectrum. We compare the dark matter models with a standard 2-step reionization theory, and examine whether the models may be distinguished using current, and future CMB observations. We consider dark matter annihilation at intermediate redshifts ($z<60$) due to halos, as well as annihilation at higher redshifts due to free particles. In order to study the effect of high redshift dark matter annihilation on CMB power spectra, it is essential to include the contribution of residual electrons (left over from recombination) to the ionization history. Dark matter halos at redshifts $z<60$ influence the low multipoles $l<20$ in the $EE$ power spectrum, while the annihilation of free particle dark matter at high redshifts $z>100$ mainly affects multipoles $l>10$.Comment: Minor corrections. Published in Phys. Rev. Replaced to reflect the published versio

The generalized Kochen-Specker theorem

A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized Kochen-Specker, Kochen-Specker and Bell theorems that shed some light on the relationship between these three theorems.Comment: 5 pages, 1 Table. A new third paragraph and an additional reference have been adde

The effect of early dark matter halos on reionization

The annihilation of dark matter particles releases energy, ionizing some of the gas in the Universe. We investigate the effect of dark matter halos on reionization. We show that the effect depends on the assumed density profile, the particle mass, and the assumed minimum halo mass. For NFW halos and typical WIMPs, we find the effect to be quite small. However, light dark matter candidates in the MeV range can contribute significantly to reionization and can make an important contribution to the measured optical depth. This effect may be used to constrain light dark matter models. We also study the effect of varying the halo density profile on reionization.Comment: Minor changes from v2. Accepted for publication in Phys. Rev.

Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits

A complete orthonormal basis of N-qutrit unitary operators drawn from the Pauli Group consists of the identity and 9^N-1 traceless operators. The traceless ones partition into 3^N+1 maximally commuting subsets (MCS's) of 3^N-1 operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order 3^N are isomorphic to all MCS's, and show how this result applies in specific cases. For two qutrits, the 80 traceless operators partition into 10 MCS's. We prove that 4 of the corresponding basis sets must be separable, while 6 must be totally entangled (and Bell-like). For three qutrits, 728 operators partition into 28 MCS's with less rigid structure allowing for the coexistence of separable, partially-entangled, and totally entangled (GHZ-like) bases. However, a minimum of 16 GHZ-like bases must occur. Every basis state is described by an N-digit trinary number consisting of the eigenvalues of N observables constructed from the corresponding MCS.Comment: LaTeX, 10 pages, 2 references adde

Men will be Men, Women will be Women: The Case of Cross-Gender Brand Extensions

The paper examines the current popularity of cross-gender brand extensions, based on its theoretical foundations in branding and gender differences in information processing strategies. We ar- gue that consumers experience a situation of gender-salience in the case of cross-gender brand extensions, resulting in gender-differen- tial responses towards the practice

Rapid-purification protocols for optical homodyning

We present a number of rapid-purification feedback protocols for optical homodyne detection of a single optical qubit. We derive first a protocol that speeds up the rate of increase of the average purity of the system, and find that like the equivalent protocol for a non-disspative measurement, this generates a deterministic evolution for the purity in the limit of strong feedback. We also consider two analogues of the Wiseman-Ralph rapid-purification protocol in this setting, and show that like that protocol they speed up the average time taken to reach a fixed level of purity. We also examine how the performance of these algorithms changes with detection efficiency, being an important practical consideration.Comment: 6 pages, revtex4, 3 eps figure

Dark matter annihilation and its effect on CMB and Hydrogen 21 cm observations

If dark matter is made up of Weakly Interacting Massive Particles, the annihilation of these particles in halos results in energy being released, some of which is absorbed by gas, causing partial ionization and heating. Dark matter annihilation may result in partial ionization and gas heating at high redshifts, even before the formation of the first stars. It is shown that early ionization results in a transfer of power to higher multipoles in the large angle CMB polarization power spectra. Future CMB experiments may be able to place constraints on certain light dark matter models. We also investigate the effect of gas heating on the expected H21 cm power spectrum. Heating by particle annihilation results in a decrease in the amplitude of the H21 cm power spectrum as the gas temperature $T$ becomes comparable to the CMB temperature $T_\gamma$, and then an increase as $T > T_\gamma$. The result is a minimum in the power spectrum at the redshift for which $T \approx T_\gamma$. Only certain models (low particle masses $\sim$ 10 GeV, or favorable halo parameters) show this effect. Within these models, observations of the H21 cm power spectrum at multiple redshifts can help us obtain constraints on dark matter particle and halo properties.Comment: We correct an error in the calculation of $\kappa$ in Eq. 6. This results in a ~ factor 2 increase in the magnitude of the results. New plots have been computed. Replaced to reflect the published versio

The Projective Line Over the Finite Quotient Ring GF(2)[xx]/<x3−x>< x^{3} - x> and Quantum Entanglement II. The Mermin "Magic" Square/Pentagram

In 1993, Mermin (Rev. Mod. Phys. 65, 803--815) gave lucid and strikingly simple proofs of the Bell-Kochen-Specker (BKS) theorem in Hilbert spaces of dimensions four and eight by making use of what has since been referred to as the Mermin(-Peres) "magic square" and the Mermin pentagram, respectively. The former is a $3 \times 3$ array of nine observables commuting pairwise in each row and column and arranged so that their product properties contradict those of the assigned eigenvalues. The latter is a set of ten observables arranged in five groups of four lying along five edges of the pentagram and characterized by similar contradiction. An interesting one-to-one correspondence between the operators of the Mermin-Peres square and the points of the projective line over the product ring ${\rm GF}(2) \otimes \rm{GF}(2)$ is established. Under this mapping, the concept "mutually commuting" translates into "mutually distant" and the distinguishing character of the third column's observables has its counterpart in the distinguished properties of the coordinates of the corresponding points, whose entries are both either zero-divisors, or units. The ten operators of the Mermin pentagram answer to a specific subset of points of the line over GF(2)[$x$]/$$. The situation here is, however, more intricate as there are two different configurations that seem to serve equally well our purpose. The first one comprises the three distinguished points of the (sub)line over GF(2), their three "Jacobson" counterparts and the four points whose both coordinates are zero-divisors; the other features the neighbourhood of the point ($1, 0$) (or, equivalently, that of ($0, 1$)). Some other ring lines that might be relevant for BKS proofs in higher dimensions are also mentioned.Comment: 6 pages, 5 figure

An Analytical Approach for Design of Microstrip Patch (MsP)

A reliable configuration of electromagnetic interactions for antenna design can yield an effective Microstrip patch (MsP) antenna. During its design, the antenna arrays involve issues with parameters (i.e., space, dimension, shape) adjustment. This problem can be tackled with an analytical approach which can help to bring better idea to design the antenna aaray. However, the realistic designs of antenna array are quite expensive while extracting computational accuracy. Thus, to have low cost computational accuracy various meta-heuristic (generic algorithm, partical swarm optimizarion) approaches are used and are considered as effective one in handling the pattern synthesis problems. Howeever, the use of meta-heuristic approaches demands thousands of functions to analyze the antenna design. This manuscript introduces an analytical approach for MsP antenna desing using MATLAB that brings optimization in handling the side lobes and optimizing the reflection as well as radiation responses. The outcomes of the design were analyzed with respect to reflection, radiation coefficients, side lobes and found effective at 10GHz as per computational cost is concern