Parasupersymmetric Quantum Mechanics with Generalized Deformed Parafermions

A superposition of bosons and generalized deformed parafermions corresponding to an arbitrary paraquantization order $p$ is considered to provide deformations of parasupersymmetric quantum mechanics. New families of parasupersymmetric Hamiltonians are constructed in connection with two examples of su(2) nonlinear deformations such as introduced by Polychronakos and Ro\v cek.Comment: 9 pages, LaTeX, no figures, to be published in Helv. Phys. Act

Tita: discovery of carbon monoxide in its atmosphere

The 3-D rotation-vibration band of carbon monoxide was identified in the near-infrared spectrum of Titan. A preliminary mixing ratio of CO/N2 = 0.00006 was determined. This result supports the probable detection of CO2 by Samuelson et al and strengthens possible analogies between the atmosphere of Titan and conditions on the primitive Earth

Monodeuterated methane in the outer Solar System. Part 3: Its abundance on Titan

The 3 nu 2 band of CH3D has been detected in spectra of Titan recorded at 1.6 microns with the Fourier Transform Spectrometer (FTS) at the 4 m telescope of the Kitt Peak National Observatory (NOAO). We have obtained a value of the CH3D/CH4 mixing ratio of 6.6 (+6.6 or -3.3) x 10 to the -4 from a comparison between the observed Titan spectra and synthetic spectra. This value is approx. 2 times higher than the value measured on Uranus (de Bergh et al. 1986) and approx. 6 times higher than on Jupiter and on Saturn (Courtin et al. 1984; de Bergh et al. 1986). It corresponds to D/H of 1.65 (+1.65 or -0.8) x 10 the -4, nominally 8 times higher than the most commonly accepted value for the protosolar D/H = 2 x 10 to the -5 (Geiss and Reeves 1981). The value we find on Titan for D/H in methane is comparable to the D/H ratio measured in terrestrial H2O

Monodeurated methane in the outer solar system. 2. Its detection on Uranus at 1.6 microns

Deuterium in the atmosphere of Uranus has been studied only via measurements of the exceedingly weak dipole lines of hydrogen-deuteride (HD) seen in the visible region of the spectrum. The other sensitive indicator of deuterium in the outer solar system is monodeuterated methane (CH3D) but the two bands normally used ot study this molecule, NU sub 2 near 2200 1/cm and NU sub 6 near 1161 1/cm, have not been detected in Uranus

Deuterium on Venus: Observations from Earth

In view of the importance of the deuterium-to-hydrogen ratio in understanding the evolutionary scenario of planetary atmospheres and its relationship to understanding the evolution of our own Earth, we undertook a series of observations designed to resolve previous observational conflicts. We observed the dark side of Venus in the 2.3 micron spectral region in search of both H2O and HDO, which would provide us with the D/H ratio in Venus' atmosphere. We identified a large number of molecular lines in the region, belonging to both molecules, and, using synthetic spectral techniques, obtained mixing ratios of 34 plus or minus 10 ppm and 1.3 plus or minus 0.2 ppm for H2O and HDO, respectively. These mixing ratios yield a D/H ratio for Venus of D/H equals 1.9 plus or minus 0.6 times 10 (exp 12) and 120 plus or minus 40 times the telluric ratio. Although the detailed interpretation is difficult, our observations confirm that the Pioneer Venus Orbiter results and establish that indeed Venus had a period in its early history in which it was very wet, perhaps not unlike the early wet period that seems to have been present on Mars, and that, in contrast to Earth, lost much of its water over geologic time

Near-infrared oxygen airglow from the Venus nightside

Groundbased imaging and spectroscopic observations of Venus reveal intense near-infrared oxygen airglow emission from the upper atmosphere and provide new constraints on the oxygen photochemistry and dynamics near the mesopause (approximately 100 km). Atomic oxygen is produced by the Photolysis of CO2 on the dayside of Venus. These atoms are transported by the general circulation, and eventually recombine to form molecular oxygen. Because this recombination reaction is exothermic, many of these molecules are created in an excited state known as O2(delta-1). The airglow is produced as these molecules emit a photon and return to their ground state. New imaging and spectroscopic observations acquired during the summer and fall of 1991 show unexpected spatial and temporal variations in the O2(delta-1) airglow. The implications of these observations for the composition and general circulation of the upper venusian atmosphere are not yet understood but they provide important new constraints on comprehensive dynamical and chemical models of the upper mesosphere and lower thermosphere of Venus

Group Theoretical Foundations of Fractional Supersymmetry

Fractional supersymmetry denotes a generalisation of supersymmetry which may be constructed using a single real generalised Grassmann variable, $\theta = \bar{\theta}, \, \theta^n = 0$, for arbitrary integer $n = 2, 3, ...$. An explicit formula is given in the case of general $n$ for the transformations that leave the theory invariant, and it is shown that these transformations possess interesting group properties. It is shown also that the two generalised derivatives that enter the theory have a geometric interpretation as generators of left and right transformations of the fractional supersymmetry group. Careful attention is paid to some technically important issues, including differentiation, that arise as a result of the peculiar nature of quantities such as $\theta$.Comment: Plain Latex, 18 page

Hydrogen atom as an eigenvalue problem in 3D spaces of constant curvature and minimal length

An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is considered from the perspective of the radial Schr\"odinger equations on 3D spaces of any (either positive, zero or negative) constant curvature. Further to Stevenson, we show in detail how to get the hypergeometric wavefunction for the hydrogen atom case. Finally, we make a comparison between the ``space curvature" effects and minimal length effects for the hydrogen spectrumComment: 6 pages, v

A new class of non-Hermitian Hamiltonians with real spectra

We construct a new class of non-Hermitian Hamiltonians with real spectra. The Hamiltonians possess one explicitly known eigenfunction.Comment: 6 page

On realizations of nonlinear Lie algebras by differential operators

We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear, quadratic and cubic cases are explicitly visited but the method works for arbitrary degrees in the polynomial functions. Multi-boson Hamiltonians are studied in the context of these ``nonlinear'' Lie algebras and some examples dealing with quantum optics are pointed out.Comment: 21 pages, Latex; New examples added in Sect.