CMB in a box: causal structure and the Fourier-Bessel expansion

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light-cone of the observer. This happens order by order in a series expansion in powers of the visibility $\gamma=e^{-\mu}$, where $\mu$ is the optical depth to Thompson scattering. We show that the CMB anisotropies are regulated by spacetime window functions which have support only inside the past light-cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. In that expansion, for each multipole $l$ there is a discrete tower of momenta $k_{i,l}$ (not a continuum) which can affect physical observables, with the smallest momenta being $k_{1,l} ~ l$. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies. (Abridged)Comment: 23 pages, 7 figure

Nonclassical rotational inertia for a supersolid under rotation

As proposed by Leggett [4], the supersolidity of a crystal is characterized by the Non Classical Rotational Inertia (NCRI) property. Using a model of quantum crystal introduced by Josserand, Pomeau and Rica [5], we prove that NCRI occurs. This is done by analyzing the ground state of the aforementioned model, which is related to a sphere packing problem, and then deriving a theoretical formula for the inertia momentum. We infer a lower estimate for the NCRI fraction, which is a landmark of supersolidity

Evidence for Ubiquitous Collimated Galactic-Scale Outflows along the Star-Forming Sequence at z~0.5

We present an analysis of the MgII 2796, 2803 and FeII 2586, 2600 absorption line profiles in individual spectra of 105 galaxies at 0.3<z<1.4. The galaxies, drawn from redshift surveys of the GOODS fields and the Extended Groth Strip, fully sample the range in star formation rates (SFRs) occupied by the star-forming sequence with stellar masses log M_*/M_sun > 9.5 at 0.3<z<0.7. Using the Doppler shifts of the MgII and FeII absorption lines as tracers of cool gas kinematics, we detect large-scale winds in 66+/-5% of the galaxies. HST/ACS imaging and our spectral analysis indicate that the outflow detection rate depends primarily on galaxy orientation: winds are detected in ~89% of galaxies having inclinations (i) <30 degrees (face-on), while the wind detection rate is only ~45% in objects having i>50 degrees (edge-on). Combined with the comparatively weak dependence of the wind detection rate on intrinsic galaxy properties, this suggests that biconical outflows are ubiquitous in normal, star-forming galaxies at z~0.5. We find that the wind velocity is correlated with host galaxy M_* at 3.4-sigma significance, while the equivalent width of the flow is correlated with host galaxy SFR at 3.5-sigma significance, suggesting that hosts with higher SFR may launch more material into outflows and/or generate a larger velocity spread for the absorbing clouds. Assuming that the gas is launched into dark matter halos with simple, isothermal density profiles, the wind velocities measured for the bulk of the cool material (~200-400 km/s) are sufficient to enable escape from the halo potentials only for the lowest-M_* systems in the sample. However, the outflows typically carry sufficient energy to reach distances of >50 kpc, and may therefore be a viable source of cool material for the massive circumgalactic medium observed around bright galaxies at z~0. [abridged]Comment: Submitted to ApJ. 61 pages, 25 figures, 4 tables, 4 appendices. Uses emulateapj forma

Chiral Fermions and Quadratic Divergences

In an approach towards naturalness without supersymmetry, renormalization properties of nonsupersymmetric abelian quiver gauge theories are studied. In the construction based on cyclic groups Z_p the gauge group is U(N)^p, the fermions are all in bifundamentals and the construction allows scalars in adjoints and bifundamentals. Only models without adjoint scalars, however, exhibit both chiral fermions and the absence of one-loop quadratic divergences in the scalar propagator.Comment: 11 page

Lower bounds for several online variants of bin packing

We consider several previously studied online variants of bin packing and prove new and improved lower bounds on the asymptotic competitive ratios for them. For that, we use a method of fully adaptive constructions. In particular, we improve the lower bound for the asymptotic competitive ratio of online square packing significantly, raising it from roughly 1.68 to above 1.75.Comment: WAOA 201

Universality in Bacterial Colonies

The emergent spatial patterns generated by growing bacterial colonies have been the focus of intense study in physics during the last twenty years. Both experimental and theoretical investigations have made possible a clear qualitative picture of the different structures that such colonies can exhibit, depending on the medium on which they are growing. However, there are relatively few quantitative descriptions of these patterns. In this paper, we use a mechanistically detailed simulation framework to measure the scaling exponents associated with the advancing fronts of bacterial colonies on hard agar substrata, aiming to discern the universality class to which the system belongs. We show that the universal behavior exhibited by the colonies can be much richer than previously reported, and we propose the possibility of up to four different sub-phases within the medium-to-high nutrient concentration regime. We hypothesize that the quenched disorder that characterizes one of these sub-phases is an emergent property of the growth and division of bacteria competing for limited space and nutrients.Comment: 12 pages, 5 figure

Finite dimensional quantizations of the (q,p) plane : new space and momentum inequalities

We present a N-dimensional quantization a la Berezin-Klauder or frame quantization of the complex plane based on overcomplete families of states (coherent states) generated by the N first harmonic oscillator eigenstates. The spectra of position and momentum operators are finite and eigenvalues are equal, up to a factor, to the zeros of Hermite polynomials. From numerical and theoretical studies of the large $N$ behavior of the product $\lambda\_m(N) \lambda\_M(N)$ of non null smallest positive and largest eigenvalues, we infer the inequality $\delta\_N(Q) \Delta\_N(Q) = \sigma\_N \overset{<}{\underset{N \to \infty}{\to}} 2 \pi$ (resp. $\delta\_N(P) \Delta\_N(P) = \sigma\_N \overset{<}{\underset{N \to \infty}{\to}} 2 \pi$) involving, in suitable units, the minimal ($\delta\_N(Q)$) and maximal ($\Delta\_N(Q)$) sizes of regions of space (resp. momentum) which are accessible to exploration within this finite-dimensional quantum framework. Interesting issues on the measurement process and connections with the finite Chern-Simons matrix model for the Quantum Hall effect are discussed

Minimum Length from Quantum Mechanics and Classical General Relativity

We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length, $l_P$. This suggests a Planck-size {\it minimum ball} of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order $l_P$. Our results imply a {\it device independent} limit on possible position measurements.Comment: 8 pages, latex, to appear in the Physical Review Letter

An Observational Determination of the Proton to Electron Mass Ratio in the Early Universe

In an effort to resolve the discrepancy between two measurements of the fundamental constant mu, the proton to electron mass ratio, at early times in the universe we reanalyze the same data used in the earlier studies. Our analysis of the molecular hydrogen absorption lines in archival VLT/UVES spectra of the damped Lyman alpha systems in the QSOs Q0347-383 and Q0405-443 yields a combined measurement of a (Delta mu)/mu value of (-7 +/- 8) x 10^{-6}, consistent with no change in the value of mu over a time span of 11.5 gigayears. Here we define (Delta mu) as (mu_z - mu_0) where mu_z is the value of mu at a redshift of z and mu_0 is the present day value. Our null result is consistent with the recent measurements of King et al. 2009, (Delta mu)/u = (2.6 +/- 3.0) x 10^{-6}, and inconsistent with the positive detection of a change in mu by Reinhold et al. 2006. Both of the previous studies and this study are based on the same data but with differing analysis methods. Improvements in the wavelength calibration over the UVES pipeline calibration is a key element in both of the null results. This leads to the conclusion that the fundamental constant mu is unchanged to an accuracy of 10^{-5} over the last 80% of the age of the universe, well into the matter dominated epoch. This limit provides constraints on models of dark energy that invoke rolling scalar fields and also limits the parameter space of Super Symmetric or string theory models of physics. New instruments, both planned and under construction, will provide opportunities to greatly improve the accuracy of these measurements.Comment: Accepted for publication in the Astrophysical Journa