Hamiltonian Simulation Using Linear Combinations of Unitary Operations

We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation algorithms based on product formulas and, most notably, scales better with the simulation error than any known Hamiltonian simulation technique. Our main tool is a general method to nearly deterministically implement linear combinations of nearby unitary operations, which we show is optimal among a large class of methods.Comment: 18 pages, 3 figure

Relation between parameters of dust and parameters of molecular and atomic gas in extragalactic star-forming regions

The relationships between atomic and molecular hydrogen and dust of various sizes in extragalactic star-forming regions are considered, based on observational data from the Spitzer and Herschel infrared space telescopes, the Very Large Array (atomic hydrogen emission) and IRAM (CO emission). The source sample consists of approximately 300 star-forming regions in 11 nearby galaxies. Aperture photometry has been applied to measure the fluxes in eight infrared bands (3.6, 4.5, 5.8, 8, 24, 70, 100, and 160$\mu$m), the atomic hydrogen (21cm) line and CO (2--1) lines. The parameters of the dust in the starforming regions were determined via synthetic-spectra fitting, such as the total dust mass, the fraction of polycyclic aromatic hydrocarbons (PAHs), etc. Comparison of the observed fluxes with the measured parameters shows that the relationships between atomic hydrogen, molecular hydrogen, and dust are different in low- and high-metallicity regions. Low-metallicity regions contain more atomic gas, but less molecular gas and dust, including PAHs. The mass of dust constitutes about $1\%$ of the mass of molecular gas in all regions considered. Fluxes produced by atomic and molecular gas do not correlate with the parameters of the stellar radiation, whereas the dust fluxes grow with increasing mean intensity of stellar radiation and the fraction of enhanced stellar radiation. The ratio of the fluxes at 8 and 24$\mu$m, which characterizes the PAH content, decreases with increasing intensity of the stellar radiation, possibly indicating evolutionary variations of the PAH content. The results confirm that the contribution of the 24$\mu$m emission to the total IR luminosity of extragalactic star-forming regions does not depend on the metallicity.Comment: Published in Astronomy Reports, 2017, vol. 61, issue

Spectra of Maser Radiation from a Turbulent, Circumnuclear Accretion Disk. III. Circular polarization

Calculations are performed for the circular polarization of maser radiation from a turbulent, Keplerian disk that is intended to represent the sub-parsec disk at the nucleus of the galaxy NGC4258. The polarization in the calculations is a result of the Zeeman effect in the regime in which the Zeeman splitting is much less than the spectral linebreadth. Plausible configurations for turbulent magnetic and velocity fields in the disk are created by statistical methods. This turbulence, along with the Keplerian velocity gradients and the blending of the three hyperfine components to form the $6_{16} - 5_{23}$ masing transition of water, are key ingredients in determining the appearance of the polarized spectra that are calculated. These spectra are quite different from the polarized spectra that would be expected for a two-level transition where there is no hyperfine structure. The effect of the hyperfine structure on the polarization is most striking in the calculations for the maser emission that represents the central (or systemic) features of NGC4258. Information about magnetic fields is inferred from observations for polarized maser radiation and bears on the structure of accretion disks.Comment: Latex, uses aastex, eucal, to be published in the Astrophysical Journa