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https://www.tau.ac.il/%7Eklafter1/258.pdf

The random walk's guide to anomalous diffusion: a fractional dynamics approach

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

/pdf/the-observation-of-gravitational-waves-from-a-binary-black-58srpupgg9.pdf

The Observation of Gravitational Waves from a Binary Black Hole Merger

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

What is Quantum Optics? Ante The Wigner Function Quantum States in Phase Space Waves a la WKB WKB Wave Functions and Berry's Phase Interference in Phase Space Applications of Interference in Phase Space Wave Packet Dynamics Quantization of the Radiation Field Quantum States of the Radiation Field Phase Space Functions Optical Interferometry Atom-Field Interaction Dynamics of Jaynes-Cummings-Paul Model State Preparation and Entanglement The Paul Trap Damping and Amplification Atom Optics in Quantized Light Fields Wigner Functions in Atom Optics Appendix Time Dependent Operators - Derivation of Equations Determining the Moyal Function - Energy Wave Functions of Harmonic Oscillator - Method of Stationary Phase - Radial Equation - Airy Function - Asymptotic Expansion of the Poisson Distribution - Area of Overlap - P-Distributions - Homodyne Detection Kernel - Effective Hamiltonian - Spontaneous Emission - A Model for the Square Root of a Delta Function - Bessel Functions

Quantum optics in phase space

This paper presents a review of both active and passive ring laser devices. The operating principles of the ring laser are developed and discussed, with special emphasis given to the problems associated with the achievement of greater sensitivity and stability. First-principle treatments of the nature of quantum noise in the ring laser gyro and various methods designed to avoid low-rotation-rate lock-in are presented. Descriptions of state-of-the-art devices and current and proposed applications (including a proposed test of metric theories of gravity using a passive cavity ring laser) are given.

The ring laser gyro

Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Because of their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this Letter we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far field of a double slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity.

Wolfgang P. Schleich

Papers

Quantum optics in phase space

The ring laser gyro

Interferometry with Bose-Einstein Condensates in Microgravity

Fundamental Systems in Quantum Optics

Quantum state engineering of the radiation field.