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

Semi-classical theory of quiet lasers. Short version

This article is the shorten version of quant-phys/0610106 with a supplemented theory and new results concerning a single-electron laser driven by a constant-potentiel battery. "Quiet (or sub-Poissonian) oscillators generate a number of dissipation events whose variance is less than the mean. It was shown in 1984 by Golubev and Sokolov that lasers driven by regular pumps are quiet in that sense. We consider in the present paper two oscillators that should exhibit in principle the same property. First, a reflex klystron, a vacuum tube operating in the microwave range of frequency. Second a laser involving a single electron permanently interacting with the field. It is unnecessary to quantize the optical field, that is, the theory is semi-classical, yet exact. As an example, the battery-driven one-electron laser delivers a detected noise of 7/8 of the shot-noise level, and is therefore sub-Poissonian. Our calculations are related to resonance-fluorescence treatments but with a different physical interpretation. Previous theories considering excited-state atoms regularly-injected in low-loss resonators, on the other hand, do require light quantization. The theory presented here is restricted to above-threshold stationary single-mode oscillators. The paper is written in such a way that readers should be able to follow it without having to refer to quantum-optics texts."Comment: Submitted to European Journal of Physic

Educational Systems, Intergenerational Mobility and Social Segmentation

We show that the very characteristics of educational systems generate social segmentation. A stylised educational framework is constructed in which everyone receives a compulsory basic education and can subsequently choose between direct working, vocational studies and university. There is a selection for entering the university which consists of a minimum human capital level at the end of basic education. In the model, an individual's human capital depends (i) on her/his parents' human capital, (ii) on her/his schooling time, and (iii) on public expenditure for education. There are three education functions corresponding to each type of study (basic, vocational, university). Divergences in total educational expenditure, in its distribution between the three studies and in the selection severity, combined with the initial distribution of human capital across individuals, can result in very different social segmentations and generate under education traps (situations in which certain dynasties remain unskilled from generation to generation) at the steady state. We finally implement a series of simulations that illustrate these findings in the cases of egalitarian and elitist educational systems. Assuming the same initial distribution of human capital between individuals, we find that the first system results in two-segment stratification, quasi income equality and no under education trap whereas the elitist system generates three segments, significant inequality and a large under education trapEducational systems; intergenerational mobility; social segmentation; under-education trap

Comment on: "Sadi Carnot on Carnot's theorem"

Carnot established in 1824 that the efficiency $\eta_{C}$ of reversible engines operating between a hot bath at absolute temperature $T_{hot}$ and a cold bath at temperature $T_{cold}$ is equal to $1-T_{cold}/T_{hot}$. Carnot particularly considered air as a working fluid and small bath-temperature differences. Plugging into Carnot's expression modern experimental values, exact agreement with modern Thermodynamics is found. However, in a recently published paper ["Sadi Carnot on Carnot's theorem", \textit{Am. J. Phys.} \textbf{70}(1), 42-47, 2002], Guemez and others consider a "modified cycle" involving two isobars that they mistakenly attribute to Carnot. They calculate an efficiency considerably lower than $\eta_{C}$ and suggest that Carnot made compensating errors. Our contention is that the Carnot theory is, to the contrary, perfectly accurate.Comment: Submitted to American Journal of Physic

Statistics of non-interacting bosons and fermions in micro-canonical, canonical and grand-canonical ensembles: A survey

The statistical properties of non-interacting bosons and fermions confined in trapping potentials are most easily obtained when the system may exchange energy and particles with a large reservoir (grand-canonical ensemble). There are circumstances, however, where the system under consideration may be considered as being isolated (micro-canonical ensemble). This paper first reviews results relating to micro-canonical ensembles. Some of them were obtained a long time ago, particularly by Khinchin in 1950. Others were obtained only recently, often motivated by experimental results relating to atomic confinement. A number of formulas are reported for the first time in the present paper. Formulas applicable to the case where the system may exchange energy but not particles with a reservoir (canonical ensemble) are derived from the micro-canonical ensemble expressions. The differences between the three ensembles tend to vanish in the so-called Thermodynamics limit, that is, when the number of particles and the volume go to infinity while the particle number density remains constant. But we are mostly interested in systems of moderate size, often referred to as being mesoscopic, where the grand-canonical formalism is not applicable. The mathematical results rest primarily on the enumeration of partitions of numbers.Comment: 18 pages, submitted to J. Phys.