Flow equations for cold Bose gases

Wederive flow equations for cold atomic gases with one macroscopically populated energy level. The generator is chosen such that the ground state decouples from all other states in the system as the renormalization group flow progresses.Wepropose a self-consistent truncation scheme for the flow equations at the level of three-body operators and show how they can be used to calculate the ground state energy of a generalN-body system. Moreover, we provide a general method to estimate the truncation error in the calculated energies. Finally, we test our scheme by benchmarking to the exactly solvable Lieb–Liniger model and find good agreement for weak and moderate interaction strengths

The role of household chaos in understanding relations between early poverty and children’s academic achievement

The following prospective longitudinal study used an epidemiological sample (N = 1,236) to consider the potential mediating role of early cumulative household chaos (6–58 months) on associations between early family income poverty (6 months) and children's academic achievement in kindergarten. Two dimensions of household chaos, disorganization and instability, were examined as mediators. Results revealed that, in the presence of household disorganization (but not instability) and relevant covariates, income poverty was no longer directly related to academic achievement. Income poverty was, however, positively related to household disorganization, which was, in turn, associated with lower academic achievement. Study results are consistent with previous research indicating that household chaos conveys some of the adverse longitudinal effects of income poverty on children's outcomes and extend previous findings specifically to academic achievement in early childhood

The epidemiology of observed temperament: Factor structure and demographic group differences

This study investigated the factor structure of observational indicators of children’s temperament that were collected across the first three years of life in the Family Life Project (N = 1205) sample. A four-factor model (activity level, fear, anger, regulation), which corresponded broadly to Rothbart’s distinction between reactivity and regulation, provided an acceptable fit the observed data. Tests of measurement invariance demonstrated that a majority of the observational indicators exhibited comparable measurement properties for male vs. female, black vs. white, and poor vs. not-poor children, which improved the generalizability of these results. Unadjusted demographic group comparisons revealed small to moderate sized differences (Cohen ds = |.23 – .42|) in temperamental reactivity and moderate to large sized differences (Cohen ds = −.64 – −.97) in regulation. Collectively, demographic variables explained more of the variation in regulation (R(2) = .25) than in reactivity (R(2) = .02 – .06). Follow-up analyses demonstrated that race differences were substantially diminished in magnitude and better accounted for by poverty. These results help to validate the distinction between temperamental reactivity and regulation using observational indicators