Operator Methods of the Parabolic Potential Barrier

The one-dimensional parabolic potential barrier dealt with in an earlier paper is re-examined from the point of view of operator methods, for the purpose of getting generalized Fock spaces.Comment: 7 pages, AmS-LaTeX, no figure

Entropy Burst from Parabolic Potentials

The change of the energy of ground state is investigated in a thermodynamical process by using the model described by one-dimensional harmonic oscillator + two-dimensional isotropic parabolic potential barrier such as $V(x,y,z)=m\omega^2 x^2/2 -m\gamma^2 (y^2+z^2)/2$. In the process where two independent many-particle systems suddenly touch with each other, it is shown that the lowest energy after the interaction can possibly be smaller than that before the interaction and then the entropy burst can occur.Comment: 6 pages, AmS-LaTeX, 1 figur

Supersymmetric Quantum Mechanics of Scattering

In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand triplet. Supersymmetric quantum mechanics for dealing with the scattering states is here proposed.Comment: 7 pages, AmS-LaTeX, no figure, v

Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers

Free energies and other thermodynamical quantities are investigated in canonical and grand canonical ensembles of statistical mechanics involving unstable states which are described by the generalized eigenstates with complex energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is applied to the systems containing parabolic potential barriers (PPB's). The entropy and energy productions from PPB systems are studied. An equilibrium for a chemical process described by reactions $A+CB\rightleftarrows AC+B$ is also discussed.Comment: 14 pages, AmS-LaTeX, no figur

Estimation of the refractive index of volcanic ash from satellite infrared sounder data

AbstractWe investigated the spectral refractive indices (RIs) of volcanic ash materials in the wavenumber range of 700–1100cm−1 using satellite infrared sounder measurements and radiative transfer calculations. The ash RIs of 10 ash clouds from eight volcanoes were evaluated (Bezymianny on 2 September 2012, Chaitén on 3 May 2008, Kelut on 14 February 2014, Kirishimayama on 27 January 2011, Kliuchevskoi on 30 June 2007 and 18 October 2013, Puyehue–Cordon Caulle on 5 June 2011, Sangeang-Api on 31 May 2014, and Sheveluch on 28 October 2010 and 18 September 2012). We elaborated on a dataset of volcanic ash measurements made by the Atmospheric Infrared Sounder (AIRS) onboard the Aqua satellite. The measured brightness temperatures in the ash cloud data revealed silicate absorption features at around 10μm. By applying atmospheric profiles from results of a global data assimilation system and using ash cloud properties (ash optical depth, effective radius, and ash cloud height) as parameters for radiative transfer calculations, least squares analyses for the observed and calculated brightness temperatures were conducted using AIRS channels in the wavenumber range of 700–1100cm−1, except for the O3 absorption channels in the range of 980–1070cm−1. Using the RIs for typical volcanic rocks in the ascending order of SiO2 content, basalt, andesite, and rhyolite, a mixture of basalt and rhyolite and a mixture of andesite and rhyolite for the ash material were considered. The volume fraction of the mixture was used as a retrieval parameter and as the ash cloud parameter. Using the estimated ash cloud parameters as fixed values, and under the assumption that the RI from the estimated volume fraction had some accuracy in the wavenumber ranges of 850–980cm−1 and 1070–1100cm−1, the RI imaginary part of each eruptive ash cloud captured by AIRS was then determined from iterative calculations at wavenumbers between 750cm−1 and 980cm−1. In the wavenumber range of 850–980cm−1, the observed brightness temperatures could be approximately simulated using the reported RIs from Pollack, Toon, and Khare (1973) for andesite, basalt, and rhyolite, and their combinations. Furthermore, some estimated RIs were consistent with the reported rock types of the volcanoes, which had been previously classified by compositional analyses in the literature. Our analysis also identified weak absorptions around 750–850cm−1, which could not be reproduced by the reported RIs. These weak absorptions were likely due to Si–O and/or Al–O vibrations, which have been proposed in reports from previous laboratory experiments for some silicate glass samples. Our results suggest that the detailed RI of volcanic ash can be determined from an analysis of satellite infrared sounder data. The RI of the ash material estimated from satellite infrared sounder data can be used to improve the ash retrieval algorithms of other satellite measurements. Furthermore, an RI retrieved by sounder measurements may provide diagnostic information regarding volcanic activity from comparisons with the ash RIs from past eruptions

Stationary Flows of the Parabolic Potential Barrier in Two Dimensions

In the two-dimensional isotropic parabolic potential barrier $V(x, y)=V_0 -m\gamma^2 (x^2+y^2)/2$, though it is a model of an unstable system in quantum mechanics, we can obtain the stationary states corresponding to the real energy eigenvalue $V_0$. Further, they are infinitely degenerate. For the first few eigenstates, we will find the stationary flows round a right angle that are expressed by the complex velocity potentials $W=\pm\gamma z^2/2$.Comment: 12 pages, AmS-LaTeX, 4 figure