Secular non-secular master equation

Redfield non-secular master equation governing relaxation of a spin in weak interaction with a thermal bath is studied. Using the fact that the relaxation follows the exponential law, we prove that in most cases the semi-secular approximation is sufficient to find the system relaxation rate. Based on this, a "secular" form of the non-secular master equation is for the first time developed which correctly set up one of most fundamental equations in relaxation investigation. This key secular form allows us to derive a general formula of the phonon-induced quantum tunneling rate which is valid for the entire range of temperature regardless of the basis. In incoherent tunneling regime and localized basis, this formula reduces to the ubiquitous incoherent tunneling rate. Meanwhile, in eigenstates basis, this tunneling rate is demonstrated to be equal to zero. From this secular form, we end the controversy surrounding the selection of basis for the secular approximation by figuring out the conditions for using this approximation in localized and eigenstates basis. Particularly, secular approximation in localized basis is justified in the regime of high temperature and small tunnel splittings. In contrast, a large ground doublet's tunnel splitting is required for the secular approximation in eigenstates basis. With these findings, this research lays a sound foundation for any treatments of the spin-phonon relaxation under any conditions provided that the non-secular master equation is relevant.Comment: 9 pages, 0 figure

Multiple relaxation times in single-molecule magnets

Multiple relaxation times detected in the ac magnetic susceptibility of several single-molecule magnets have been always assigned to extrinsic factors, such as nonequivalent magnetic centers or effects of intermolecular interactions in the crystal. By solving quantum relaxation equations, we prove that the observed multiple relaxation times can be of intramolecular origin and can show up even in single-ion metal complexes. For the latter a remarkably good description of the coexistent two relaxation times is demonstrated on several experimental examples. This proves the relevance of the intramolecular mechanism of multiple relaxation times in such systems, which is even easier justified in polynuclear magnetic complexes.Comment: 5 pages, 5 figure

Medium Resolution Near-Infrared Spectra of the Host Galaxies of Nearby Quasars

We present medium resolution near-infrared host galaxy spectra of low redshift quasars, PG 0844 + 349 (z=0.064), PG 1226 + 023 (z=0.158), and PG 1426+015 (z=0.086). The observations were done by using the Infrared Camera and Spectrograph (IRCS) at the Subaru 8.2 m telescope. The full width at half maximum of the point spread function was about 0.3 arcsec by operations of an adaptive optics system, which can effectively resolve the quasar spectra from the host galaxy spectra. We spent up to several hours per target and developed data reduction methods to reduce the systematic noises of the telluric emissions and absorptions. From the obtained spectra, we identified absorption features of Mg I (1.503 um), Si I (1.589 um) and CO (6-3) (1.619 um), and measured the velocity dispersions of PG 0844 + 349 to be 132+/-110 km s-1 and PG 1426 + 015 to be 264+/-215 km s-1. By using an M_BH-sigma relation of elliptical galaxies, we derived the black hole (BH) mass of PG 0844+349, log(M_BH/M_SUN) = 7.7+/-5.5 and PG 1426+015, log(M_BH/M_SUN) = 9.0+/-7.5. These values are consistent with the BH mass values from broad emission lines with an assumption of a virial factor of 5.5.Comment: 16 pages, 5 figure

DETERMINATION OF VARIABLE LAW OF THE TURBULENT DIFFUSION PARAMETERS WITH TIME INTERVAL IN THE AIR ENVIRONMENT IN VIETNAM

Joint Research on Environmental Science and Technology for the Eart

Firm-level corruption: Unravelling sand from grease

This paper adds to the recent literature on firm-level corruption by relying on rich data including detailed information on the purpose and amounts of bribe payments among Vietnamese micro, small, and medium firms. Using industry-location averages to instrument for firm-level bribe payments in both a cross-sectional and a panel setting, we provide evidence of a large and significant positive association between corruption and firm performance. We further show that the type of bribe payment does matter: only the payments that can arguably be considered 'voluntary' (rather than extortive) drive this association