Fluorescence from a few electrons

Systems containing few Fermions (e.g., electrons) are of great current interest. Fluorescence occurs when electrons drop from one level to another without changing spin. Only electron gases in a state of equilibrium are considered. When the system may exchange electrons with a large reservoir, the electron-gas fluorescence is easily obtained from the well-known Fermi-Dirac distribution. But this is not so when the number of electrons in the system is prevented from varying, as is the case for isolated systems and for systems that are in thermal contact with electrical insulators such as diamond. Our accurate expressions rest on the assumption that single-electron energy levels are evenly spaced, and that energy coupling and spin coupling between electrons are small. These assumptions are shown to be realistic for many systems. Fluorescence from short, nearly isolated, quantum wires is predicted to drop abruptly in the visible, a result not predicted by the Fermi-Dirac distribution. Our exact formulas are based on restricted and unrestricted partitions of integers. The method is considerably simpler than the ones proposed earlier, which are based on second quantization and contour integration.Comment: 10 pages, 3 figures, RevTe

Global integration of the Schr\"odinger equation within the wave operator formalism: The role of the effective Hamiltonian in multidimensional active spaces

A global solution of the Schr\"odinger equation, obtained recently within the wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A: Math. Theor. 48, 225205 (2015)], is generalized to take into account the case of multidimensional active spaces. An iterative algorithm is derived to obtain the Fourier series of the evolution operator issuing from a given multidimensional active subspace and then the effective Hamiltonian corresponding to the model space is computed and analysed as a measure of the cyclic character of the dynamics. Studies of the laser controlled dynamics of diatomic models clearly show that a multidimensional active space is required if the wavefunction escapes too far from the initial subspace. A suitable choice of the multidimensional active space, including the initial and target states, increases the cyclic character and avoids divergences occuring when one-dimensional active spaces are used. The method is also proven to be efficient in describing dissipative processes such as photodissociation.Comment: 33 pages, 11 figure

Detection of a branched alkyl molecule in the interstellar medium: iso-propyl cyanide

The largest non-cyclic molecules detected in the interstellar medium (ISM) are organic with a straight-chain carbon backbone. We report an interstellar detection of a branched alkyl molecule, iso-propyl cyanide (i-C3H7CN), with an abundance 0.4 times that of its straight-chain structural isomer. This detection suggests that branched carbon-chain molecules may be generally abundant in the ISM. Our astrochemical model indicates that both isomers are produced within or upon dust grain ice mantles through the addition of molecular radicals, albeit via differing reaction pathways. The production of iso-propyl cyanide appears to require the addition of a functional group to a non-terminal carbon in the chain. Its detection therefore bodes well for the presence in the ISM of amino acids, for which such side-chain structure is a key characteristic.Comment: This is the author's version of the work. It is posted here by permission of the AAAS for non-commercial use. The definitive version was published in Science 345, 1584 (2014), doi:10.1126/science.125667

Complex organic molecules in the interstellar medium: IRAM 30 m line survey of Sagittarius B2(N) and (M)

The discovery of amino acids in meteorites and the detection of glycine in samples returned from a comet to Earth suggest that the interstellar chemistry is capable of producing such complex organic molecules. Our goal is to investigate the degree of chemical complexity that can be reached in the ISM. We performed an unbiased, spectral line survey toward Sgr B2(N) and (M) with the IRAM 30m telescope in the 3mm window. The spectra were analyzed with a simple radiative transfer model that assumes LTE but takes optical depth effects into account. About 3675 and 945 spectral lines with a peak signal-to-noise ratio higher than 4 are detected toward N and M, i.e. about 102 and 26 lines per GHz, respectively. This represents an increase by about a factor of 2 over previous surveys of Sgr B2. About 70% and 47% of the lines detected toward N and M are identified and assigned to 56 and 46 distinct molecules as well as to 66 and 54 less abundant isotopologues of these molecules, respectively. We also report the detection of transitions from 59 and 24 catalog entries corresponding to vibrationally or torsionally excited states of some of these molecules, respectively. Excitation temperatures and column densities were derived for each species but should be used with caution. Among the detected molecules, aminoacetonitrile, n-propyl cyanide, and ethyl formate were reported for the first time in space based on this survey, as were 5 rare isotopologues of vinyl cyanide, cyanoacetylene, and hydrogen cyanide. We also report the detection of transitions from within 12 new vib. or tors. excited states of known molecules. Although the large number of unidentified lines may still allow future identification of new molecules, we expect most of these lines to belong to vib. or tors. excited states or to rare isotopologues of known molecules for which spectroscopic predictions are currently missing. (abridged)Comment: Accepted for publication in A&A. 266 pages (39 pages of text), 111 tables, 8 figure

Development of a general time-dependent absorbing potential for the constrained adiabatic trajectory method

The Constrained Adiabatic Trajectory Method (CATM) allows us to compute solutions of the time-dependent Schr\"odinger equation using the Floquet formalism and Fourier decomposition, using matrix manipulation within a non-orthogonal basis set, provided that suitable constraints can be applied to the initial conditions for the Floquet eigenstate. A general form is derived for the inherent absorbing potential, which can reproduce any dispersed boundary conditions. This new artificial potential acting over an additional time interval transforms any wavefunction into a desired state, with an error involving exponentially decreasing factors. Thus a CATM propagation can be separated into several steps to limit the size of the required Fourier basis. This approach is illustrated by some calculations for the $H_2^+$ molecular ion illuminated by a laser pulse.Comment: 8 pages, 7 figure

La modélisation stochastique des pluies horaires et leur transformation en débits pour la prédétermination des crues

Pour étudier les distributions de fréquences des variables hydrologiques (pluies et débits) au pas de temps horaire, une méthodologie associant un générateur de chroniques de pluies horaires et un modèle conceptuel global de transformation de la pluie en débit a été développée. Sur une période de simulation donnée, la méthode génère une collection de scénarios de crues vraisemblables utilisée en prédétermination des risques hydrologiques. Les distributions de fréquences des variables hydrologiques sont construites empiriquement à partir des événements de pluies et de crues générés. L'extrapolation des distributions de fréquences des variables hydrologiques vers les fréquences rares se fait de façon empirique en augmentant la période de simulation, et non plus sur l'ajustement direct des distributions observées. Le principe de cette méthode (appelée SHYPRE : Simulation d'HYdrogrammes pour la PREdétermination) est donc d'utiliser les observations pour décrire le phénomène, afin de le reproduire statistiquement et de s'affranchir ainsi du manque d'observation. Son utilisation permet une estimation originale des quantiles de crues de fréquences courantes à rares et présente l'intérêt d'obtenir une information temporelle complète sur ces crues. De plus, on montre que l'approche fournit une estimation de quantiles de crues bien plus robuste que les ajustements statistiques des distributions observées, même pour les événements de fréquences courantes. Cette robustesse provient d'une meilleure prise en compte de l'information pluviométrique et de la stabilité de la paramétrisation du modèle pluie-débit.A statistical approach encompassing a stochastic model to generate hourly rainfall and rainfall runoff was used to study frequency distributions of hydrologic variables. The method generates numerous different flood events over a given simulation period to evaluate hydrologic risks. Entitled Simulated HYdrographs for flood PRobability Estimation (SHYPRE), it makes use of observed values to describe hydrological phenomena and successfully reproduces observed-value statistics. Frequency distributions of hydrologic variables are built empirically from model-generated rainfall and flood events. Extrapolation of these frequency distributions to rare frequencies is performed by simulation over longer periods, rather than by direct fit of theoretical probability distributions over observed values. This approach yields different estimations of flood quantiles for common to rare frequencies as well as complete temporal flood data. Moreover, SHYPRE estimates of flood quantiles are more stable than statistical distributions fitted onto observed values, even for frequent events. The improvement stems from better use of rainfall data and from the parametric stability of the rainfall model and rainfall-runoff model