5,011 research outputs found

    Photon number variance in isolated cavities

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    We consider a strictly isolated single-mode optical cavity resonating at angular frequency omega containing atoms whose one-electron level energies are supposed to be: hbar*omega, 2*hbar*omega,...B*hbar\omega, and m photons. If initially the atoms are in their highest energy state and m=0, we find that at equilibrium: variance(m)/mean(m)=(B+1)/6, indicating that the internal field statistics is sub-Poissonian if the number of atomic levels B does not exceed 4. Remarkably, this result does not depend on the number of atoms, nor on the number of electrons that each atom incorporates. Our result has application to the statistics of the light emitted by pulsed lasers and nuclear magnetic resonance. On the mathematical side, the result is based on the restricted partitions of integers.Comment: 4 pages, to be submitted to Journal of Physics

    Generating connected acyclic digraphs uniformly at random

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    We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non necessarily connected.Comment: 6 page

    On Classical Ideal Gases

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    The ideal gas laws are derived from the democritian concept of corpuscles moving in vacuum plus a principle of simplicity, namely that these laws are independent of the laws of motion aside from the law of energy conservation. A single corpuscle in contact with a heat bath and submitted to a zz and tt-invariant force −w-w is considered, in which case corpuscle distinguishability is irrelevant. The non-relativistic approximation is made only in examples. Some of the end results are known but the method appears to be novel. The mathematics being elementary the present paper should facilitate the understanding of the ideal-gas law and more generally of classical thermodynamics. It supplements importantly a previously published paper: The stability of ideal gases is proven from the expressions obtained for the force exerted by the corpuscle on the two end pistons of a cylinder, and the internal energy. We evaluate the entropy increase that occurs when the wall separating two cylinders is removed and show that the entropy remains the same when the separation is restored. The entropy increment may be defined at the ratio of heat entering into the system and temperature when the number of corpuscles (0 or 1) is fixed. In general the entropy is defined as the average value of ln⁡(p)\ln(p) where pp denotes the probability of a given state. Generalization to zz-dependent weights, or equivalently to arbitrary static potentials, is made.Comment: Generalization of previous versions to questions of stabilit

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

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    Carnot established in 1824 that the efficiency ηC\eta_{C} of reversible engines operating between a hot bath at absolute temperature ThotT_{hot} and a cold bath at temperature TcoldT_{cold} is equal to 1−Tcold/Thot1-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 ηC\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
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