Monte Carlo Simulation of Laser Diodes Sub-Poissonian Light Generation

When laser diodes are driven by high-impedance electrical sources the variance of the number of photo-detection events counted over large time durations is less than the average number of events (sub-Poissonian light). The paper presents a Monte Carlo simulation that keeps track of each level occupancy (0 or 1) in the conduction and valence bands, and of the number of light quanta in the optical cavity. When there is good electron-lattice thermal contact the electron and hole temperatures remain equal to that of the lattice. In that case, elementary laser-diode noise theory results are accurately reproduced by the simulation. But when the thermal contact is poor (or, almost equivalently, at high power levels) new effects occur (spectral-hole burning, temperature fluctuations, statistical fluctuations of the optical gain) that are difficult to handle theoretically. Our numerical simulation shows that the frequency domain over which the photo-current spectral density is below the shot-noise level becomes narrower as the optical power increases.Comment: 22 pages, 3 figures, 1 table, submitted to Optical and Quantum Electronic

Sheepskin or Prozac: The Causal Effect of Education on Mental Health

Mental illness is associated with large costs to individuals and society. Education improves various health outcomes but little work has been done on mental illness. To obtain unbiased estimates of the effect of education on mental health, we rely on a rich longitudinal dataset that contains health information from childhood to adulthood and thus allow us to control for fixed effects in mental health. We measure two health outcomes: malaise score and depression and estimate the extensive and intensive margins of education on mental health using various estimators. For all estimators, accounting for the endogeneity of education augments its protecting effect on mental health. We find that the effect of education is greater at mid-level of qualifications, for women and for individuals at greater risk of mental illness. The effects of education are observed at all ages, additionally education also reduces the transition to depression. These results suggest substantial returns to education in term of improved mental health.Returns to education, mental health

Two-level laser light statistics

The statistics of the light emitted by two-level lasers is evaluated on the basis of generalized rate equations. According to that approach, all fluctuations are interpreted as being caused by the jumps that occur in active and detecting atoms. The intra-cavity Fano factor and the photo-current spectral density are obtained analytically for Poissonian and quiet pumps. The algebra is simple and the formulas hold for small as well as large pumping rates. Lasers exhibit excess noise at low pumping levels.Comment: 9 pages, 3 figures, in Optics Communication format (elsevier

Neutron Stars as Dark Matter Probes

We examine whether the accretion of dark matter onto neutron stars could ever have any visible external effects. Captured dark matter which subsequently annihilates will heat the neutron stars, although it seems the effect will be too small to heat close neutron stars at an observable rate whilst those at the galactic centre are obscured by dust. Non-annihilating dark matter would accumulate at the centre of the neutron star. In a very dense region of dark matter such as that which may be found at the centre of the galaxy, a neutron star might accrete enough to cause it to collapse within a period of time less than the age of the Universe. We calculate what value of the stable dark matter-nucleon cross section would cause this to occur for a large range of masses.Comment: 8 pages, 7 figure

Transport of phosphorus in a sewage plume

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1997.Includes bibliographical references (leaves 40-41).by Arnaud L. Morange.M.Eng

On homotopies with triple points of classical knots

We consider a knot homotopy as a cylinder in 4-space. An ordinary triple point $p$ of the cylinder is called {\em coherent} if all three branches intersect at $p$ pairwise with the same index. A {\em triple unknotting} of a classical knot $K$ is a homotopy which connects $K$ with the trivial knot and which has as singularities only coherent triple points. We give a new formula for the first Vassiliev invariant $v_2(K)$ by using triple unknottings. As a corollary we obtain a very simple proof of the fact that passing a coherent triple point always changes the knot type. As another corollary we show that there are triple unknottings which are not homotopic as triple unknottings even if we allow more complicated singularities to appear in the homotopy of the homotopy.Comment: 10 pages, 13 figures, bugs in figures correcte

Rate-equation approach to atomic-laser light statistics

We consider three- and four-level atomic lasers that are either incoherently (unidirectionally) or coherently (bidirectionally) pumped, the single-mode cavity being resonant with the laser transition. The intra-cavity Fano factor and the photo-current spectral density are evaluated on the basis of rate equations. According to that approach, fluctuations are caused by jumps in active and detecting atoms. The algebra is considerably simpler than the one required by Quantum-Optics treatments. Whenever a comparison can be made, the expressions obtained coincide. The conditions under which the output light exhibits sub-Poissonian statistics are considered in detail. Analytical results, based on linearization, are verified by comparison with Monte Carlo simulations. An essentially exhaustive investigation of sub-Poissonian light generation by three- and four-level atoms lasers has been performed. Only special forms were reported earlier.Comment: 9 pages, 7 figures, RevTeX

Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections

We consider a stochastic partial differential equation with two logarithmic nonlinearities, with two reflections at 1 and -1 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a space-time white noise, contains a bi-Laplacian in the drift. The lack of the maximum principle for the bi-Laplacian generates difficulties for the classical penalization method, which uses a crucial monotonicity property. Being inspired by the works of Debussche, Gouden\`ege and Zambotti, we obtain existence and uniqueness of solution for initial conditions in the interval $(-1,1)$. Finally, we prove that the unique invariant measure is ergodic, and we give a result of exponential mixing

The distant galaxy cluster CL0016+16: X-ray analysis up to R200R_{200}

To study the mass distribution of galaxy clusters up to their Virial radius, CL0016+16 seems to be a good candidate,since it is a bright massive cluster, previously considered as being dynamically relaxed. Using XMM-Newton observations of CL0016+16, we performed a careful X-ray background analysis, and we detected convincingly its X-ray emission up to $R_{200}$. We then studied its dynamical state with a detailed 2D temperature and surface brightness analysis of the inner part of the cluster. Using the assumption of both spherical symmetry and hydrostatic equilibrium (HE) we can determine the main cluster parameters: total mass, temperature profile, surface brightness profile and $\beta$-parameter. We also build a temperature map which clearly exhibits departure from spherical symmetry in the centre. To estimate the influence of these perturbations onto our total mass estimate, we also compute the total mass in the framework of the HE approach, but this time with various temperature profiles obtained in different directions. These various total mass estimates are consistent with each other. The temperature perturbations are clear signatures of ongoing merger activity. We also find significant residuals after subtracting the emissivity map by a 2D $\beta$-model fit. We conclude that, although CL0016+16 shows clear signs of merger activity and departure from spherical symmetry in the centre, its X-ray emissivity can be detected up to $R_{200}$ and the corresponding mass $M_{200}$ can be computed directly. It is therefore a good candidate to study cosmological scaling laws as predicted by the theory.Comment: 11 pages, 17 figures, Accepted for publication in A&