Expectations for the Difference Between Local and Global Measurements of the Hubble Constant

There are irreducible differences between the Hubble constant measured locally and the global value. They are due to density perturbations and finite sample volume (cosmic variance) and finite number of objects in the sample (sampling variance). We quantify these differences for a suite of COBE-normalized CDM models that are consistent with the observed large-scale structure. For small samples of objects that only extend out to 10,000 km/sec, the variance can approach 4%. For the largest samples of Type Ia supernovae (SNeIa), which include about 40 objects and extend out to almost 40,000 km/sec, the variance is 1-2% and is dominated by sampling variance. Sampling and cosmic variance may be an important consideration in comparing local determinations of the Hubble constant with precision determinations of the global value that will be made from high-resolution maps of CBR anisotropy.Comment: 10 pages, Latex, 2 figures, version accepted for Ap.

Hilbert's 16th Problem for Quadratic Systems. New Methods Based on a Transformation to the Lienard Equation

Fractionally-quadratic transformations which reduce any two-dimensional quadratic system to the special Lienard equation are introduced. Existence criteria of cycles are obtained

Evidence of slow-light effects from rotary drag of structured beams

Self-pumped slow light, typically observed within laser gain media, is created by an intense pump field. By observing the rotation of a structured laser beam upon transmission through a spinning ruby window, we show that the slowing effect applies equally to both the dark and bright regions of the incident beam. This result is incompatible with slow-light models based on simple pulse-reshaping arising from optical bleaching. Instead, the slow-light effect arises from the long upper-state lifetime of the ruby and a saturation of the absorption, from which the Kramers–Kronig relation gives a highly dispersive phase index and a correspondingly high group index

Entanglement and quantum phase transitions

We examine several well known quantum spin models and categorize behavior of pairwise entanglement at quantum phase transitions. A unified picture on the connection between the entanglement and quantum phase transition is given.Comment: 4 pages, 3 figure