In-in formalism on tunneling background: multi-dimensional quantum mechanics

We reformulate quantum tunneling in a multi-dimensional system where the tunneling sector is non-linearly coupled to oscillators. The WKB wave function is explicitly constructed under the assumption that the system was in the ground state before tunneling. We find that the quantum state after tunneling can be expressed in the language of the conventional in-in formalism. Some implications of the result to cosmology are discussed.Comment: 13 pages, 3 figure

Working Later in Illinois: Work Schedules, Incomes and Parents Access to Child Care

New research using federal government data shows that substantial numbers of Illinoisans work nonstandard schedules. Some 41 percent or about 2.5 million Illinois employees work either weekends or predominately non-daytime hours. The larger portion works weekends, but 19 percent or about 1.2 million employees work mostly non-daytime hours. In families with children under age 14, including single parent families and two-parent families with both parents employed, 42 percent work nonstandard hours. While nonstandard work schedules are found in some higher income occupations in Illinois such as nurses and doctors, they are more commonly concentrated in occupations that pay below the typical Illinois income, such as retail sales and building cleaning occupations. The trend, moreover, is probably upward: In the ten occupations with the largest projected job growth, 48 percent of employees work nonstandard schedules. Among the substantial challenges nonstandard work schedules present to Illinois working parents, one is finding suitable child care. According to state data, relatively few center-based and licensed home child care programs in Illinois offer care during evening, night or weekend hours. Many working parents, then, must respond to the mismatch between child care and nonstandard work schedules in one of two ways. They might stagger their work schedules so that one parent is always free for child care. This is obviously an option only for families with two parents. Other parents must find another relative, friend or neighbor to provide informal child care. (In this case parents must still coordinate their child care and work schedules with that informal provider.) Working nonstandard schedules, then, tends to force working parents to use either staggered parental care or informal family, friend or neighbor care. Lower earnings in jobs with nonstandard work schedules and the high cost of child care programs also tend to push parents toward staggering their work schedules or using informal child care. According to Illinois data, center-based and licensed home child care for one infant averages a prohibitive 15 percent of the typical family income (25 percent for an infant and a three-year old). Since family, friend and neighbor child care tends to be substantially cheaper than center and licensed home programs, working parents are likely to favor such informal care for reasons of cost as well as schedule. Data show that in fact a majority of children in Illinois do receive informal care from relatives, friends and neighbors rather than licensed or center-based care. Many children probably receive staggered parental care, although we do not have good data on this practice. Findings of the new research are consistent with the view that Illinois parents with fewer employment opportunities must accept nonstandard work schedules offered to them. For example, Illinois parents with lower than average earnings are more likely to work nonstandard schedules

Electrical safety requirements: Implications for the module designer

Commercial photovoltaic array installations, which include residential and intermediate applications, are subject to building and electrical codes and to product safety standards. The National Electrical Code (NEC) Article 690, titled Solar Photovoltaic Systems, contains provisions defining acceptable levels of system safety and emphasizes the system design and its installation. The Underwriters Laboratories, Inc. (UL), document titled: Proposed First Edition of the Standard for Flat Plate Photovoltaic Modules and Panels, UL-1703, identifies module and panel construction requirements that ensure product safety. Together these documents describe requirements intended to minimize hazards such as shock and fire. Although initial focus of these requirements is on single crystal silicon modules, they are generic in nature, and are equally applicable to high voltage ( 30 Vdc), multikilowatt, thin film systems. A major safety concern is insulation breakdown within the module or array wiring system, or discontinuities within the electrical conductors. These failures can result in ground faults, in circuit arcs, or exposure to hazardous electrical parts. Safeguards are discussed

The critical radiation intensity for direct collapse black hole formation: dependence on the radiation spectral shape

It has been proposed that supermassive black holes (SMBHs) are originated from direct-collapse black holes (DCBHs) that are formed at z gtrsim 10 in the primordial gas in the case that H2 cooling is suppressed by strong external radiation. In this work, we study the critical specific intensity J^crit required for DCBH formation for various radiation spectral shapes by a series of one-zone calculations of a collapsing primordial- gas cloud. We calculate the critical specific intensity at the Lyman-Werner (LW) bands J^crit_LW,21 (in units of 10^-21 erg s^-1 Hz^-1 sr^-1 cm^-2) for realistic spectra of metal-poor galaxies. We find J^crit is not sensitive to the age or metallicity for the constant star formation galaxies with J^crit_LW,21 = 1300-1400, while J^crit decreases as galaxies become older or more metal-enriched for the instantaneous starburst galaxies. However, such dependence for the instantaneous starburst galaxies is weak for the young or extremely metal-poor galaxies: J^crit_LW,21 = 1000-1400 for the young galaxies and J^crit_LW,21 approx 1400 for the extremely metal-poor galaxies. The typical value of J^crit for the realistic spectra is higher than those expected in the literature, which affects the estimated DCBH number density n_DCBH. By extrapolating the result of Dijkstra, Ferrara and Mesinger, we obtain n_DCBH sim 10^-10 cMpc^-3 at z = 10, although there is still large uncertainty in this estimation.Comment: 11 pages, 6 figures, submitted to MNRA