Born-Oppenheimer study of two-component few-particle systems under one-dimensional confinement

The energy spectrum, atom-dimer scattering length, and atom-trimer scattering length for systems of three and four ultracold atoms with $\delta$-function interactions in one dimension are presented as a function of the relative mass ratio of the interacting atoms. The Born-Oppenheimer approach is used to treat three-body ("HHL") systems of one light and two heavy atoms, as well as four-body ("HHHL") systems of one light and three heavy atoms. Zero-range interactions of arbitrary strength are assumed between different atoms, but the heavy atoms are assumed to be noninteracting among themselves. Both fermionic and bosonic heavy atoms are considered.Comment: 22 pages, 6 figures. Includes both positive and negative parity cases for the four-body secto

2022-1 A Partial Identification Approach to Identifying the Determinants of Human Capital Accumulation: An Application to Teachers

This paper views teacher quality through the human capital perspective. Teacher quality exhibits substantial growth over teachers’ careers, but why it improves is not well understood. I use a human capital production function nesting On-the-Job-Training (OJT) and Learning-by-Doing (LBD) and experimental variation from Glewwe et al. (2010), a teacher incentive pay experiment in Kenya, to discern the presence and relative importance of these forces. The identified set for the OJT and LBD components has a closed-form solution, which depends on experimentally estimated average treatment effects. The results provide evidence of an LBD component, as well as an informative upper bound on the OJT component

2012-3 Competition in Public School Districts: Charter School Entry, Student Sorting, and School Input Determination

I develop and estimate an equilibrium model of charter school entry, student sorting, and endogenous school inputs in public school markets using administrative student- and school-level data from North Carolina for 1998–2001. In the model, students differ by ability, and both charter and public schools make input decisions to test score production functions to affect the ability distribution of attendant students. The model successfully fits key endogenous outcomes as observed in the data: (1) charter schools enter larger markets and markets where they would have higher per-pupil resources, (2) charter schools and public schools in markets in which charter schools are present both choose higher input levels than public schools in markets where there are no charters, and (3) charter schools have the highest average test scores, followed by public schools in markets with charter school competition, followed by public schools in monopoly markets. I use the estimated model to simulate changes in the test score distribution for three counterfactual scenarios: (1) ban charter schools, (2) lift the currently binding statewide cap on the number of charter schools, and (3) equate charter and public school per-pupil resources. In the first and second counterfactuals, charter school entry increases test scores for students who would attend charters by one fifth of a standard deviation. Test scores for public school students in markets with charter schools increase marginally. Equating charter and public school capital triples the fraction of markets with charters and increases the test scores of students attending charters over the monopoly outcome by an even larger amount

Few-Boson Processes in the Presence of an Attractive Impurity under One-Dimensional Confinement

We consider a few-boson system confined to one dimension with a single distinguishable particle of lesser mass. All particle interactions are modeled with $\delta$-functions, but due to the mass imbalance the problem is nonintegrable. Universal few-body binding energies, atom-dimer and atom-trimer scattering lengths are all calculated in terms of two parameters, namely the mass ratio: $m_{\text{L}}/m_{\text{H}}$, and ratio $g_{\text{HH}}/g_{\text{HL}}$ of the $\delta$-function couplings. We specifically identify the values of these ratios for which the atom-dimer or atom-trimer scattering lengths vanish or diverge. We identify regions in this parameter space in which various few-body inelastic process become energetically allowed. In the Tonks-Girardeau limit ($g_{\text{HH}}\rightarrow \infty$), our results are relevant to experiments involving trapped fermions with an impurity atom

The Inner Revolution: Shuddhi and the Reinvention of Hinduism

The Shuddhi movement of the late 19th century was a religious revolutionary movement that aimed to intrinsically restructure and transform the Hinduism and Hindu society into a more socially equalized and religiously universal system. It was a quest to reconstruct Hindu religious and social identity in response to socioeconomic modernism and challenges from Christian and Islamic proselytization. The first phase of the movement lasted from the 1880s to the late 1910s and was defined by a persistent struggle with orthodox society to transform Hinduism by opening its doors to induct and assimilate returning and new converts. The second phase of Shuddhi began in the early 1920s with the emergence of a consensus between the orthodox and the Arya-led reformers, who expanded the Shuddhi movement to confront the challenges presented by Islam and Christianity; this phase ended in 1947