Coherent and squeezed states in black-hole evaporation

In earlier Letters, we adopted a complex approach to quantum processes in the formation and evaporation of black holes. Taking Feynman's $+i\epsilon$ prescription, rather than than one of the more usual approaches, we calculated the quantum amplitude (not just the probability density) for final weak-field configurations following gravitational collapse to a black hole with subsequent evaporation. What we have done is to find quantum amplitudes relating to a pure state at late times following black-hole matter collapse. Such pure states are then shown to be susceptible to a description in terms of coherent and squeezed states - in practice, this description is not very different from that for the well-known highly-squeezed final state of the relic radiation background in inflationary cosmology. The simplest such collapse model involves Einstein gravity with a massless scalar field. The Feynman approach involves making the boundary-value problem for gravity and a massless scalar field well-posed. To define this, let T be the proper-time separation, measured at spatial infinity, between two space-like hypersurfaces on which initial (collapse) and final (evaporation) data are posed. Then, in this approach, one rotates T by a complex phase exp(-i\delta) into the lower half-plane. In an adiabatic approximation, the resulting quantum amplitude may be expressed in terms of generalised coherent states of the quantum oscillator, and a physical interpretation is given. A squeezed-state representation, as above, then follows

On the cohomology rings of tree braid groups

Let $\Gamma$ be a finite connected graph. The (unlabelled) configuration space $UC^n \Gamma$ of $n$ points on $\Gamma$ is the space of $n$-element subsets of $\Gamma$. The $n$-strand braid group of $\Gamma$, denoted $B_n\Gamma$, is the fundamental group of $UC^n \Gamma$. We use the methods and results of our paper "Discrete Morse theory and graph braid groups" to get a partial description of the cohomology rings $H^*(B_n T)$, where $T$ is a tree. Our results are then used to prove that $B_n T$ is a right-angled Artin group if and only if $T$ is linear or $n<4$. This gives a large number of counterexamples to Ghrist's conjecture that braid groups of planar graphs are right-angled Artin groups.Comment: 25 pages, 7 figures. Revised version, accepted by the Journal of Pure and Applied Algebr

Potential for a new muon g-2 experiment

A new experiment to measure the muon g-2 factor is proposed. We suppose the sensitivity of this experiment to be about 0.03 ppm. The developed experiment can be performed on an ordinary storage ring with a noncontinuous field created by usual magnets. When the total length of straight sections of the ring is appropriate, the spin rotation frequency becomes almost independent of the particle momentum. In this case, a high-precision measurement of an average magnetic field can be carried out with polarized proton beams. A muon beam energy can be arbitrary. Possibilities to avoid a betatron resonance are analyzed and corrections to the g-2 frequency are considered.Comment: 5 pages, 1 figur

Leaving the Street In Brief

This issue of P/PV In Brief focuses on Lauren J. Kotloff's recent report, Leaving the Street: Young Fathers Move from Hustling to Legitimate Work. Based on an in-depth interview study of participants in P/PVs Fathers at Work initiative, the report provides a rare glimpse inside the lives of young urban men with criminal records, exploring how they got involved with hustling, their experiences in the labor market and their feelings about fatherhood.Leaving the Street In Brief describes the four distinct groups that emerged in P/PVs study (the Reluctant Hustlers, the Ambitious Workers, the Reluctant Workers and the Committed Hustlers) and presents early findings from the Fathers at Work evaluation. It also touches on the full report's recommendations for programs serving young fathers

Coherent integration

Coherent integration which is a digital filtering process and was applied to MST radar observations is discussed. It is simple to implement with either hardware or software and is appropriate for the very narrow band signals usually received by MST radars. By filtering the signal before performing spectral processing, the computations required for FFT or similar analysis are greatly reduced. Coherent integration does not increase the signal-to-noise ratio per unit bandwidth in the signal band. It filters out much of the wideband noise, which could also be done by full FFT processing of the raw signal