Tentative Appraisal of Compatibility of Small-Scale CMB Anisotropy Detections in the Context of COBE-DMR-Normalized Open and Flat Λ\Lambda CDM Cosmogonies

Goodness-of-fit statistics are used to quantitatively establish the compatibility of CMB anisotropy predictions in a wide range of DMR-normalized, open and spatially-flat $\Lambda$, CDM cosmogonies with the set of all presently available small-scale CMB anisotropy detection data. Conclusions regarding model viability depend sensitively on the prescription used to account for the 1$\sigma$ uncertainty in the assumed value of the DMR normalization, except for low-density, $\Omega_0 \sim 0.3$ -- 0.4, open models which are compatible with the data for all prescriptions used. While large baryon-density (\Omega_B \gap 0.0175 h^{-2}), old (t_0 \gap 15 -- 16 Gyr), low-density ($\Omega_0 \sim 0.2$ -- 0.4), flat-$\Lambda$ models might be incompatible, no model is incompatible with the data for all prescriptions. In fact, some open models seem to fit the data better than should be expected, and this might be an indication that some error bars are mildly overconservative.Comment: 15 page PostScript file, including 6 included figures. Also available via anonymous ftp from ftp://astro.caltech.edu/users/kmg/chi.p

Spectrum of Eleven-dimensional Supergravity on a PP-wave Background

We calculate the spectrum of the linearized supergravity around the maximally supersymmetric pp-wave background in eleven dimensions. The resulting spectrum agrees with that of zero-mode Hamiltonian of a supermembrane theory on the pp-wave background. We also discuss the connection with the Kaluza-Klein zero modes of AdS_4 x S^7 background.Comment: 17 pages, no figures, LaTeX2e, typos correcte

{\delta}N formalism

Precise understanding of nonlinear evolution of cosmological perturbations during inflation is necessary for the correct interpretation of measurements of non-Gaussian correlations in the cosmic microwave background and the large-scale structure of the universe. The "{\delta}N formalism" is a popular and powerful technique for computing non-linear evolution of cosmological perturbations on large scales. In particular, it enables us to compute the curvature perturbation, {\zeta}, on large scales without actually solving perturbed field equations. However, people often wonder why this is the case. In order for this approach to be valid, the perturbed Hamiltonian constraint and matter-field equations on large scales must, with a suitable choice of coordinates, take on the same forms as the corresponding unperturbed equations. We find that this is possible when (1) the unperturbed metric is given by a homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker metric; and (2) on large scales and with a suitable choice of coordinates, one can ignore the shift vector (g0i) as well as time-dependence of tensor perturbations to gij/a2(t) of the perturbed metric. While the first condition has to be assumed a priori, the second condition can be met when (3) the anisotropic stress becomes negligible on large scales. However, in order to explicitly show that the second condition follows from the third condition, one has to use gravitational field equations, and thus this statement may depend on the details of theory of gravitation. Finally, as the {\delta}N formalism uses only the Hamiltonian constraint and matter-field equations, it does not a priori respect the momentum constraint. We show that the violation of the momentum constraint only yields a decaying mode solution for {\zeta}, and the violation vanishes when the slow-roll conditions are satisfied.Comment: 10 page

Effect of nonnegativity on estimation errors in one-qubit state tomography with finite data

We analyze the behavior of estimation errors evaluated by two loss functions, the Hilbert-Schmidt distance and infidelity, in one-qubit state tomography with finite data. We show numerically that there can be a large gap between the estimation errors and those predicted by an asymptotic analysis. The origin of this discrepancy is the existence of the boundary in the state space imposed by the requirement that density matrices be nonnegative (positive semidefinite). We derive an explicit form of a function reproducing the behavior of the estimation errors with high accuracy by introducing two approximations: a Gaussian approximation of the multinomial distributions of outcomes, and linearizing the boundary. This function gives us an intuition for the behavior of the expected losses for finite data sets. We show that this function can be used to determine the amount of data necessary for the estimation to be treated reliably with the asymptotic theory. We give an explicit expression for this amount, which exhibits strong sensitivity to the true quantum state as well as the choice of measurement.Comment: 9 pages, 4 figures, One figure (FIG. 1) is added to the previous version, and some typos are correcte

Quantum Monte Carlo method using phase-free random walks with Slater determinants

We develop a quantum Monte Carlo method for many fermions that allows the use of any one-particle basis. It projects out the ground state by random walks in the space of Slater determinants. An approximate approach is formulated to control the phase problem with a trial wave function $|\Psi_T>$. Using plane-wave basis and non-local pseudopotentials, we apply the method to Si atom, dimer, and 2, 16, 54 atom (216 electrons) bulk supercells. Single Slater determinant wave functions from density functional theory calculations were used as $|\Psi_T>$ with no additional optimization. The calculated binding energy of Si2 and cohesive energy of bulk Si are in excellent agreement with experiments and are comparable to the best existing theoretical results.Comment: 5 pages, Latex, with 1 fi

Nonlinear Evolution of Cosmic Magnetic Fields and Cosmic Microwave Background Anisotropies

In this work we investigate the effects of the primordial magnetic fields on cosmic microwave background anisotropies (CMB). Based on cosmological magnetohydrodynamic (MHD) simulations we calculate the CMB anisotropy spectra and polarization induced by fluid fluctuations (Alfv\'en modes) generated by primordial magnetic fields. The strongest effect on the CMB spectra comes from the transition epoch from a turbulent regime to a viscous regime. The balance between magnetic and kinetic energy until the onset of the viscous regime provides a one to one relation between the comoving coherence length $L$ and the comoving magnetic field strength $B$, such as $L \sim 30 (B/10^{-9}{\rm G})^3 \rm pc$. The resulting CMB temperature and polarization anisotropies are somewhat different from the ones previously obtained by using linear perturbation theory. Our calculation gives a constraint on the magnetic field strength in the intermediate scale of CMB observations. Upper limits are set by WMAP and BOOMERANG results for comoving magnetic field strength of $B < 28 \rm nG$ with a comoving coherence length of $L > 0.7 \rm Mpc$ for the most extreme case, or $B 0.8 \rm Mpc$ for the most conservative case.Comment: accepted for publication in Phys. Rev.

Study on the Levitation and Restoring Force Characteristics of the Improved HTS-permanent Magnet Hybrid Magnetic Bearing

AbstractWe have developed the hybrid magnetic bearing using permanent magnets and high temperature bulk super conductor (HTS). In this system, the permanent magnet has ring type structure so that the permanent magnet and the HTS can be set to the stator. The pinning force of the HTS is used for the levitation and the guidance. Repulsive force of the permanent magnets was used in the conventional hybrid system. However the restoring force in the guidance direction of the conventional hybrid system decreases by the side slip force of the permanent magnets. In this research, attractive force of permanent magnets is used for increasing the load weight in the guidance direction.In this paper, influence of the hybrid system on the static characteristics of the rotor is studied. Three-dimensional numerical analysis of the linkage flux (in the levitation and the guidance direction) in the HTS is undertaken. The stator side permanent magnet increases the linkage flux of the levitation direction. Therefore in the hybrid system the linkage flux of the levitation direction increases. The levitation and restoring force of the rotor is measured. The levitation force of the hybrid system becomes smaller than that of the non-hybrid one by attractive force. The rotor in the hybrid system is supported by the pinning force and attractive force. The restoring force of the hybrid system becomes larger than that of the non-hybrid one because of increasing the linkage flux of the levitation direction

Mean Field Phase Diagram of SU(2)xSU(2) Lattice Higgs-Yukawa Model at Finite Lambda

The phase diagram of an SU(2)_L x SU(2)_R lattice Higgs-Yukawa model with finite lambda is constructed using mean field theory. The phase diagram bears a superficial resemblance to that for infinite lambda, however as lambda is decreased the paramagnetic region shrinks in size. For small lambda the phase transitions remain second order, and no new first order transitions are seen.Comment: 9 pages, 3 postscript figures, RevTex. To appear in PR

Some results about zero-cycles on abelian and semi-abelian varieties

In this short note we extend some results obtained in \cite{Gazaki2015}. First, we prove that for an abelian variety $A$ with good ordinary reduction over a finite extension of $\mathbb{Q}_p$ with $p$ an odd prime, the Albanese kernel of $A$ is the direct sum of its maximal divisible subgroup and a torsion group. Second, for a semi-abelian variety $G$ over a perfect field $k$, we construct a decreasing integral filtration $\{F^r\}_{r\geq 0}$ of Suslin's singular homology group, $H_0^{sing}(G)$, such that the successive quotients are isomorphic to a certain Somekawa K-group.Comment: 13 page