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

Extended Jaynes-Cummings models and (quasi)-exact solvability

The original Jaynes-Cummings model is described by a Hamiltonian which is exactly solvable. Here we extend this model by several types of interactions leading to a nonhermitian operator which doesn't satisfy the physical condition of space-time reflection symmetry (PT symmetry). However the new Hamiltonians are either exactly solvable admitting an entirely real spectrum or quasi exactly solvable with a real algebraic part of their spectrum.Comment: 16 pages, 3 figures, discussion extended, one section adde

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.

The Surface Compositions of Triton, Pluto, and Charon

Neptune's satellite Triton, and the planet-satellite binary Pluto and Charon, are the most distant planetary bodies on which ices have been directly detected. Triton and Pluto have very similar dimensions and mean densities, suggesting a similar or common origin. Through earth-based spectroscopic observations in the near-infrared, solid N2, CH4, and CO have been found on both bodies, with the additional molecule C02 on Triton. N2 dominates both surfaces, although the coverage is not spatially uniform. On Triton, the CH4 and CO are mostly or entirely frozen in the N2 matrix, while CO2 may be spatially segregated. On Pluto, some CH4 and the CO are frozen in the N2 matrix, but there is evidence for additional CH4 in a pure state, perhaps lying as a lag deposit on a subsurface layer of N2. Despite their compositional and dimensional similarities, Pluto and Triton are quite different from one another in detail. Additional hydrocarbons and other volatile ices have been sought spectroscopically but not yet have been detected. The only molecule identified on Pluto's satellite Charon is solid H2O, but the spectroscopic data are of low precision and admit the presence of other ices such as CH4

Polynomial algebras and exact solutions of general quantum non-linear optical models I: Two-mode boson systems

We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe ansatz) solutions to a class of 2-mode boson systems, including the Boson-Einstein Condensate models as special cases. Up to an overall factor, the eigenfunctions of the 2-mode boson systems are given by polynomials whose roots are solutions of the associated Bethe ansatz equations. The corresponding eigenvalues are expressed in terms of these roots. We also establish the spectral equivalence between the BEC models and certain quasi-exactly solvable Sch\"ordinger potentials.Comment: 20 pages, final version to appear in J. Phys. A: Math. Theor

On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space

A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. The examples considered include simple harmonic oscillators with complex angular frequencies, Stark(Zeeman) effect with complex electric(magnetic) field, non-hermitian general quadratic form of N boson(fermion) operators, symmetric and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian Haldane-Shastry spin-chain and Lipkin-Meshkov-Glick model.Comment: 29 pages, revtex, minor changes, version to appear in Journal of Physics A(v3

On some nonlinear extensions of the angular momentum algebra

Deformations of the Lie algebras so(4), so(3,1), and e(3) that leave their so(3) subalgebra undeformed and preserve their coset structure are considered. It is shown that such deformed algebras are associative for any choice of the deformation parameters. Their Casimir operators are obtained and some of their unitary irreducible representations are constructed. For vanishing deformation, the latter go over into those of the corresponding Lie algebras that contain each of the so(3) unitary irreducible representations at most once. It is also proved that similar deformations of the Lie algebras su(3), sl(3,R), and of the semidirect sum of an abelian algebra t(5) and so(3) do not lead to associative algebras.Comment: 22 pages, plain TeX + preprint.sty, no figures, to appear in J.Phys.

Master equations for effective Hamiltonians

We reelaborate on a general method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the su(2) algebra that arises as the dynamical symmetry of the original model. When some physical parameter (usually related to the dispersive limit) becomes small, we immediately get a diagonal effective Hamiltonian that represents correctly the dynamics for arbitrary states and long times. We apply the same technique to obtain how the noise terms in the original model transform under this scheme, providing a systematic way of including damping effects in processes described in terms of effective Hamiltonians.Comment: 10 pages, no figure