Phase Operator Problem and Macroscopic Extension of Quantum Mechanics

To find the Hermitian phase operatorof a single-mode electromagnetic field in quantum mechanics, the Schroedinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian phase operator is shown to exist on the extended Hilbert space. This operator is naturally considered as the controversial limit of the approximate phase operators on finite dimensional spaces proposed by Pegg and Barnett. The spectral measure of this operator is a Naimark extension of the optimal probability operator-valued measure for the phase parameter found by Helstrom. Eventually, the two promising approaches to the statistics of the phase in quantum mechanics is unified by means of the Hermitian phase operator in the macroscopic extension of the Schroedinger representation.Comment: 26 pages, LaTeX, no figures, to appear in Ann. Phys. (N.Y.

H, C, and N isotopic compositions of Hayabusa category 3 organic samples

Since isotopic ratios of H, C, and N are sensitive indicators for determining extraterrestrial organics, we have measured these isotopes of Hayabusa category 3 organic samples of RB-QD04-0047-02, RA-QD02-0120, and RB-QD04-0001 with ion imaging using a NanoSIMS ion microprobe. All samples have H, C, and N isotopic compositions that are terrestrial within errors (approximately ±50‰ for H, approximately ±9‰ for C, and approximately ±2‰ for N). None of these samples contain micrometer-sized hot spots with anomalous H, C, and N isotopic compositions, unlike previous isotope data for extraterrestrial organic materials, i.e., insoluble organic matters (IOMs) and nano-globules in chondrites, interplanetary dust particles (IDPs), and cometary dust particles. We, therefore, cannot conclude whether these Hayabusa category 3 samples are terrestrial contaminants or extraterrestrial materials because of the H, C, and N isotopic data. A coordinated study using microanalysis techniques including Fourier transform infrared spectrometry (FT-IR), time-of-flight secondary ion mass spectrometry (ToF-SIMS), NanoSIMS ion microprobe, Raman spectroscopy, X-ray absorption near edge spectroscopy (XANES), and transmission electron microscopy/scanning transmission electron microscopy (TEM/STEM) is required to characterize Hayabusa category 3 samples in more detail for exploring their origin and nature.This research was supported by the JSPS Strategic Fund for Strengthening Leading-edge Research and Development to the JAMSTEC

Optical Properties of (162173) 1999 JU3: In Preparation for the JAXA Hayabusa 2 Sample Return Mission

We investigated the magnitude-phase relation of (162173) 1999 JU3, a target asteroid for the JAXA Hayabusa 2 sample return mission. We initially employed the international Astronomical Union's H-G formalism but found that it fits less well using a single set of parameters. To improve the inadequate fit, we employed two photometric functions, the Shevchenko and Hapke functions. With the Shevchenko function, we found that the magnitude-phase relation exhibits linear behavior in a wide phase angle range (alpha = 5-75 deg) and shows weak nonlinear opposition brightening at alpha< 5 deg, providing a more reliable absolute magnitude of Hv = 19.25 +- 0.03. The phase slope (0.039 +- 0.001 mag/deg) and opposition effect amplitude (parameterized by the ratio of intensity at alpha=0.3 deg to that at alpha=5 deg, I(0.3)/I(5)=1.31+-0.05) are consistent with those of typical C-type asteroids. We also attempted to determine the parameters for the Hapke model, which are applicable for constructing the surface reflectance map with the Hayabusa 2 onboard cameras. Although we could not constrain the full set of Hapke parameters, we obtained possible values, w=0.041, g=-0.38, B0=1.43, and h=0.050, assuming a surface roughness parameter theta=20 deg. By combining our photometric study with a thermal model of the asteroid (Mueller et al. in preparation), we obtained a geometric albedo of pv = 0.047 +- 0.003, phase integral q = 0.32 +- 0.03, and Bond albedo AB = 0.014 +- 0.002, which are commensurate with the values for common C-type asteroids.Comment: 27 pages, 4 figure, accepted for publication in the Astrophysical Journa

ToF-SIMS analysis of carbonaceous particles in the sample catcher of the Hayabusa spacecraft

Three carbonaceous category 3 particles (RA-QD02-0180, RB-QD04-0037-01, and RB-QD04-0047-02) returned in the sample catcher from the Hayabusa spacecraft were analyzed by time of flight-secondary ion mass spectrometry (ToF-SIMS) to establish an analytical procedure for determination of their origins. By the different analytical schemes, the three particles gave distinct elemental and molecular ions, in which the organic carbons commonly appear to be associated with nitrogen, silicon, and/or fluorine. The particles could be debris of silicon rubber and fluorinated compounds and are therefore man-made artifacts rather than natural organic matter