Intermediate wave-function statistics

We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Seba billiards. First, we show that these eigenfunctions are not quantum ergodic, and calculate the corresponding limit distribution. Second, we find that they can be strongly scarred by short periodic orbits, and construct sequences of states which have such a limit. Our results are illustrated by numerical computations.Comment: 4 pages, 3 figures. Final versio

No quantum ergodicity for star graphs

We investigate statistical properties of the eigenfunctions of the Schrodinger operator on families of star graphs with incommensurate bond lengths. We show that these eigenfunctions are not quantum ergodic in the limit as the number of bonds tends to infinity by finding an observable for which the quantum matrix elements do not converge to the classical average. We further show that for a given fixed graph there are subsequences of eigenfunctions which localise on pairs of bonds. We describe how to construct such subsequences explicitly. These constructions are analogous to scars on short unstable periodic orbits.Comment: 26 pages, 5 figure

Probing neutrino masses with CMB lensing extraction

We evaluate the ability of future cosmic microwave background (CMB) experiments to measure the power spectrum of large scale structure using quadratic estimators of the weak lensing deflection field. We calculate the sensitivity of upcoming CMB experiments such as BICEP, QUaD, BRAIN, ClOVER and PLANCK to the non-zero total neutrino mass M_nu indicated by current neutrino oscillation data. We find that these experiments greatly benefit from lensing extraction techniques, improving their one-sigma sensitivity to M_nu by a factor of order four. The combination of data from PLANCK and the SAMPAN mini-satellite project would lead to sigma(M_nu) = 0.1 eV, while a value as small as sigma(M_nu) = 0.035 eV is within the reach of a space mission based on bolometers with a passively cooled 3-4 m aperture telescope, representative of the most ambitious projects currently under investigation. We show that our results are robust not only considering possible difficulties in subtracting astrophysical foregrounds from the primary CMB signal but also when the minimal cosmological model (Lambda Mixed Dark Matter) is generalized in order to include a possible scalar tilt running, a constant equation of state parameter for the dark energy and/or extra relativistic degrees of freedom.Comment: 13 pages, 4 figures. One new figure and references added. Version accepted for publicatio

Spectral Statistics of "Cellular" Billiards

For a bounded planar domain $\Omega^0$ whose boundary contains a number of flat pieces $\Gamma_i$ we consider a family of non-symmetric billiards $\Omega$ constructed by patching several copies of $\Omega^0$ along $\Gamma_i$'s. It is demonstrated that the length spectrum of the periodic orbits in $\Omega$ is degenerate with the multiplicities determined by a matrix group $G$. We study the energy spectrum of the corresponding quantum billiard problem in $\Omega$ and show that it can be split in a number of uncorrelated subspectra corresponding to a set of irreducible representations $\alpha$ of $G$. Assuming that the classical dynamics in $\Omega^0$ are chaotic, we derive a semiclassical trace formula for each spectral component and show that their energy level statistics are the same as in standard Random Matrix ensembles. Depending on whether ${\alpha}$ is real, pseudo-real or complex, the spectrum has either Gaussian Orthogonal, Gaussian Symplectic or Gaussian Unitary types of statistics, respectively.Comment: 18 pages, 4 figure

CMB Beam Systematics: Impact on Lensing Parameter Estimation

The CMB's B-mode polarization provides a handle on several cosmological parameters most notably the tensor-to-scalar ratio, $r$, and is sensitive to parameters which govern the growth of large scale structure (LSS) and evolution of the gravitational potential. The primordial gravitational-wave- and secondary lensing-induced B-mode signals are very weak and therefore prone to various foregrounds and systematics. In this work we use Fisher-matrix-based estimations and apply, for the first time, Monte-Carlo Markov Chain (MCMC) simulations to determine the effect of beam systematics on the inferred cosmological parameters from five upcoming experiments: PLANCK, POLARBEAR, SPIDER, QUIET+CLOVER and CMBPOL. We consider beam systematics which couple the beam substructure to the gradient of temperature anisotropy and polarization (differential beamwidth, pointing and ellipticity) and beam systematics due to differential beam normalization (differential gain) and orientation (beam rotation) of the polarization-sensitive axes (the latter two effects are insensitive to the beam substructure). We determine allowable levels of beam systematics for given tolerances on the induced parameter errors and check for possible biases in the inferred parameters concomitant with potential increases in the statistical uncertainty. All our results are scaled to the 'worst case scenario'. In this case and for our tolerance levels, the beam rotation should not exceed the few-degree to sub-degree level, typical ellipticity is required to be 1% level, the differential gain allowed level is a few parts in $10^{3}$ to $10^{4}$, differential beamwidth upper limits are of the sub-percent level and differential pointing should not exceed the few- to sub-arcsec level.Comment: 19 pages, 4 figures, 13 tables. Version matches published versio

CMB Polarization Systematics Due to Beam Asymmetry: Impact on Cosmological Birefringence

The standard cosmological model is assumed to respect parity symmetry. Under this assumption the cross-correlations of the CMB's temperature anisotropy and `gradient'-like polarization, with the `curl'-like polarization identically vanish over the full sky. However, extensions of the standard model which allow for light scalar field or axion coupling to the electromagnetic field, or coupling to the Riemann gravitational field-strength, as well as other modifications of field theories, may induce a rotation of the CMB polarization plane on cosmological scales and manifest itself as nonvanishing TB and EB cross-correlations. Recently, the degree of parity violation (reflected in polarization rotation) was constrained using data from BOOMERANG, WMAP and QUAD. Forecasts have been made for near-future experiments (e.g. PLANCK) to further constrain parity- and Lorentz-violating terms in the fundamental interactions of nature. Here we consider a real-world effect induced by a class of telescope beam systematics which can mimic the rotation of polarization plane or otherwise induce nonvanishing TB and EB correlations. In particular, adopting the viewpoint that the primary target of future experiments will be the inflationary B-mode signal, we assume the beam-systematics of the upcoming PLANCK and POLARBEAR experiments are optimized towards this goal, and explore the implications of the allowed levels of beam systematics on the resulting precision of polarization-rotation measurements.Comment: 9 pages. Minor typos corrected. Matches published version in PRD Vol. 79 No. 1