Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu

Chip-Scale, Sub-Hz Fundamental Sub-kHz Integral Linewidth 780 nm Laser through Self-Injection-Locking a Fabry-P\'erot laser to an Ultra-High Q Integrated Resonator

Today's state of the art precision experiments in quantum, gravimetry, navigation, time keeping, and fundamental science have strict requirements on the level and spectral distribution of laser frequency noise. For example, the laser interaction with atoms and qubits requires ultra-low frequency noise at multiple offset frequencies due to hyperfine atomic transitions, motional sidebands, and fast pulse sequencing. Chip-scale integration of lasers that meet these requirements is essential for reliability, low-cost, and weight. Here, we demonstrate a significant advancement in atomic precision light sources by realizing a chip-scale, low-cost, 780 nm laser for rubidium atom applications with record-low 640 mHz (white noise floor at 0.2 Hz$^2$/Hz) fundamental and 732 Hz integral linewidths and a frequency noise that is multiple orders of magnitude lower than previous hybrid and heterogeneous self-injection locked 780 nm lasers and lower noise than bulk microresonator implementations. The laser is a Fabry-P\'erot laser diode self-injection locked to an ultra-high Q photonic integrated silicon nitride resonator. This performance is enabled by a 145 million resonator Q with a 30 dB extinction ratio, the highest Q at 780 nm, to the best of our knowledge. We analyze the impact of our frequency noise on specific atomic applications including atomic frequency references, Rydberg quantum gates, and cold atom gravimeters. The photonic integrated resonator is fabricated using a CMOS foundry-compatible, wafer-scale process, with demonstrated integration of other components showing promise for a full system-on-a-chip. This performance is scalable to other visible atomic wavelengths, opening the door to a variety of transitions across many atomic species and enabling low-power, compact, ultra-low noise lasers impacting applications including quantum sensing, computing, clocks and more

A depression before a bump in the highest energy cosmic ray spectrum

We re-examine the interaction of ultra high energy nuclei with the microwave background radiation. We find that the giant dipole resonance leaves a new signature in the differential energy spectrum of iron sources located around 3 Mpc: A depression before the bump which is followed by the expected cutoff.Comment: revisited version, 5 pages RevTex, 5 figure

A simple analytical model for dark matter halo structure and adiabatic contraction

A simple analytical model for describing inner parts of dark matter halo is considered. It is assumed that dark matter density is power-law. The model deals with dark matter distribution function in phase space of adiabatic invariants (radial action and angular momentum). Two variants are considered for the angular part of the distribution function: narrow and broad distribution. The model allows to describe explicitly the process of adiabatic contraction of halo due to change of gravitational potential caused by condensation of baryonic matter in the centre. The modification of dark matter density in the centre is calculated, and is it shown that the standard algorithm of adiabatic contraction calculation overestimates the compressed halo density, especially in the case of strong radial anisotropy.Comment: 5 pages, 3 figures. v3 - major improvements, another halo model introduced, discussion extende

Single-parameter non-adiabatic quantized charge pumping

Controlled charge pumping in an AlGaAs/GaAs gated nanowire by single-parameter modulation is studied experimentally and theoretically. Transfer of integral multiples of the elementary charge per modulation cycle is clearly demonstrated. A simple theoretical model shows that such a quantized current can be generated via loading and unloading of a dynamic quasi-bound state. It demonstrates that non-adiabatic blockade of unwanted tunnel events can obliterate the requirement of having at least two phase-shifted periodic signals to realize quantized pumping. The simple configuration without multiple pumping signals might find wide application in metrological experiments and quantum electronics.Comment: 4 pages, 4 figure

The Role of a Hot Gas Environment on the Evolution of Galaxies

Most spiral galaxies are found in galaxy groups with low velocity dispersions; most E/S0 galaxies are found in galaxy groups with relatively high velocity dispersions. The mass of the hot gas we can observe in the E/S0 groups via their thermal X-ray emission is, on average, as much as the baryonic mass of the galaxies in these groups. By comparison, galaxy clusters have as much or more hot gas than stellar mass. Hot gas in S-rich groups, however, is of low enough temperature for its X-ray emission to suffer heavy absorption due to Galactic HI and related observational effects, and hence is hard to detect. We postulate that such lower temperature hot gas does exist in low velocity dispersion, S-rich groups, and explore the consequences of this assumption. For a wide range of metallicity and density, hot gas in S-rich groups can cool in far less than a Hubble time. If such gas exists and can cool, especially when interacting with HI in existing galaxies, then it can help link together a number of disparate observations, both Galactic and extragalactic, that are otherwise difficult to understand.Comment: 16 pages with one figure. ApJ Letters, in pres

A Causal Order for Spacetimes with C0C^0 Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves

We recast the tools of ``global causal analysis'' in accord with an approach to the subject animated by two distinctive features: a thoroughgoing reliance on order-theoretic concepts, and a utilization of the Vietoris topology for the space of closed subsets of a compact set. We are led to work with a new causal relation which we call $K^+$, and in terms of it we formulate extended definitions of concepts like causal curve and global hyperbolicity. In particular we prove that, in a spacetime \M which is free of causal cycles, one may define a causal curve simply as a compact connected subset of \M which is linearly ordered by $K^+$. Our definitions all make sense for arbitrary $C^0$ metrics (and even for certain metrics which fail to be invertible in places). Using this feature, we prove for a general $C^0$ metric, the familiar theorem that the space of causal curves between any two compact subsets of a globally hyperbolic spacetime is compact. We feel that our approach, in addition to yielding a more general theorem, simplifies and clarifies the reasoning involved. Our results have application in a recent positive energy theorem, and may also prove useful in the study of topology change. We have tried to make our treatment self-contained by including proofs of all the facts we use which are not widely available in reference works on topology and differential geometry.Comment: Two small revisions to accomodate errors brought to our attention by R.S. Garcia. No change to chief results. 33 page

Electromagnetic Cascades and Cascade Nucleosynthesis in the Early Universe

We describe a calculation of electromagnetic cascading in radiation and matter in the early universe initiated by the decay of massive particles or by some other process. We have used a combination of Monte Carlo and numerical techniques which enables us to use exact cross sections, where known, for all the relevant processes. In cascades initiated after the epoch of big bang nucleosynthesis $\gamma$-rays in the cascades will photodisintegrate $^4$He, producing $^3$He and deuterium. Using the observed $^3$He and deuterium abundances we are able to place constraints on the cascade energy deposition as a function of cosmic time. In the case of the decay of massive primordial particles, we place limits on the density of massive primordial particles as a function of their mean decay time, and on the expected intensity of decay neutrinos.Comment: compressed and uuencoded postscript. We now include a comparison with previous work of the photon spectrum in the cascade and the limits we calculate for the density of massive particles. The method of calculation of photon spectra at low energies has been improved. Most figures are revised. Our conclusions are substantially unchange

Inverse Compton Scattering as the Source of Diffuse EUV Emission in the Coma Cluster of Galaxies

We have examined the hypothesis that the majority of the diffuse EUV flux in the Coma cluster is due to inverse Compton scattering of low energy cosmic ray electrons (0.16 < epsilon < 0.31 GeV) against the 3K black-body background. We present data on the two-dimensional spatial distribution of the EUV flux and show that these data provide strong support for a non-thermal origin for the EUV flux. However, we show that this emission cannot be produced by an extrapolation to lower energies of the observed synchrotron radio emitting electrons and an additional component of low energy cosmic ray electrons is required.Comment: 11 pages, 5 figure