Work in Progress: Do Women Score Lower Than Men on Computer Engineering Exams?

Women have long been underrepresented in undergraduate engineering programs. Women may drop out of engineering programs when they become discouraged by low exam scores. In this project, we examine whether women earn lower exam scores than men and whether Dweck's model of self-theories explains the difference. Dweck proposed two categories for individuals beliefs about intelligence: incremental theories and entity theories. Dweck found that women are more likely to be entity theorists than men. In our study, we found that the difference between exam averages between women and men, and between entity and incremental theorists were not statistically significant.published or submitted for publicationis peer reviewe

Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain

A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a charge density wave initial state, and theoretical works identified a set of many-body "scar states" showing nonthermal behavior in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at \emph{infinite temperature} that can be represented exactly as matrix product states with finite bond dimension, for both periodic boundary conditions (two exact $E = 0$ states) and open boundary conditions (two $E = 0$ states and one each $E = \pm \sqrt{2}$). This discovery explicitly demonstrates violation of strong eigenstate thermalization hypothesis in this model and uncovers exact quantum many-body scar states. These states show signatures of translational symmetry breaking with period-2 bond-centered pattern, despite being in one dimension at infinite temperature. We show that the nearby many-body scar states can be well approximated as "quasiparticle excitations" on top of our exact $E = 0$ scar states, and propose a quasiparticle explanation of the strong oscillations observed in experiments.Comment: Published version. In addition to (v2): (1) Add additional proofs to the exact scar states and intuitions behind SMA and MMA to the appendices. (2) Add entanglement scaling of SMA and MMA to the appendice

Explicit construction of quasi-conserved local operator of translationally invariant non-integrable quantum spin chain in prethermalization

We numerically construct translationally invariant quasi-conserved operators with maximum range M which best-commute with a non-integrable quantum spin chain Hamiltonian, up to M = 12. In the large coupling limit, we find that the residual norm of the commutator of the quasi-conserved operator decays exponentially with its maximum range M at small M, and turns into a slower decay at larger M. This quasi-conserved operator can be understood as a dressed total "spin-z" operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same maximum range. We also examine the operator inverse participation ratio of the operator, which suggests its localization in the operator Hilbert space. The operator also shows almost exponentially decaying profile at short distance, while the long-distance behavior is not clear due to limitations of our numerical calculation. Further dynamical simulation confirms that the prethermalization-equilibrated values are described by a generalized Gibbs ensemble that includes such quasi-conserved operator.Comment: 22 pages with 13 pages of main text, 9 figures and 5 appendices (published version

Migration, Social Security, and Economic Growth

This paper studies the effect of population aging on economic performance in an overlapping-generations model with international migration. Fertility is endogenized so that immigrants and natives can have different fertility rates. Fertility is an important determinant to the tax burden of social security since it affects the quantity and quality of future tax payers. We find that introducing immigrants into the economy can reduce the tax burden of social security. If life expectancy (or the replacement ratio) is high enough, the growth rate of GDP per worker for an economy with international migration will be higher than for a closed economy. Regarding migration policies, our numerical results indicate that economic growth rate of GDP per worker will first decrease then increase as the flow of immigrants increases. Increasing the quality of immigrants will enhance economic growth.Economic growth; Fertility; Migration; Social security.