13,761 research outputs found
Photon number variance in isolated cavities
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
Global geometry of T2 symmetric spacetimes with weak regularity
We define the class of weakly regular spacetimes with T2 symmetry, and
investigate their global geometry structure. We formulate the initial value
problem for the Einstein vacuum equations with weak regularity, and establish
the existence of a global foliation by the level sets of the area R of the
orbits of symmetry, so that each leaf can be regarded as an initial
hypersurface. Except for the flat Kasner spacetimes which are known explicitly,
R takes all positive values. Our weak regularity assumptions only require that
the gradient of R is continuous while the metric coefficients belong to the
Sobolev space H1 (or have even less regularity).Comment: 5 page
Productivity and R&D at the Firm Level in French Manufacturing
In a companion study to that of Griliches and Mairesse for the United States, we have investigated the relationship between output, labor, and physical and R&D capital during the 1972-1977 period for a sample of 182 R&D performing firms in the French nnufacturing industries. Our results are quite comparable to those obtained for the U.S. The relationship between firm productivity and R&D appears both strong and robust in the cross-sectional dimension of the data; it is less so in the time dimension. However, the within-firm estimates are still significant and of a likely order of magnitude.In this respect, they are more satisfactory than the U.S. ones. We show that this is largely due to a better measurement of the variables: (1) the fact that we can use a value-added measure of output instead of sales (or equivalently that we include materials among the factors of the production function); (2) the fact that we can correct the measures of labor, physical capital and output for the double counting or expensing out of the labor, capital and materials components of R&D expenditures.
On Classical Ideal Gases
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 and
-invariant force 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
where denotes the probability of a given state. Generalization to
-dependent weights, or equivalently to arbitrary static potentials, is made.Comment: Generalization of previous versions to questions of stabilit
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.
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