Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations

Quantum virial expansion provides an ideal tool to investigate the high-temperature properties of a strongly correlated Fermi gas. Here, we construct the virial expansion in the presence of spin population imbalance. Up to the third order, we calculate the high-temperature free energy of a unitary Fermi gas as a function of spin imbalance, with infinitely large, attractive or repulsive interactions. In the latter repulsive case, we show that there is no itinerant ferromagnetism when quantum virial expansion is applicable. We therefore estimate an upper bound for the ferromagnetic transition temperature $T_{c}$. For a harmonically trapped Fermi gas at unitarity, we find that $(T_{c})_{uppper}<T_{F}$, where $T_{F}$ is the Fermi temperature at the center of the trap. Our result for the high-temperature equations of state may confront future high-precision thermodynamic measurements.Comment: 7 pages, 5 figures, accepted in Phys. Rev.

Preservice Teacher Learning to Help English Language Learners Make Sense of Mathematics

This study investigates how preservice teachers (PST) help English language learners (ELLs) understand cognitive demanding mathematical problems using complicated language use. Three mathematics PSTs worked with ELLs in one-on-one settings while receiving individual interventions. The strategies they implemented were analyzed based on four categories: mathematical content, culture/life experience, mathematical/cognitive process, and mathematical/contextual language. As time evolved, all of the PSTs began to integrate life connection strategies and various visuals that are closely related to mathematical situations, which they learned during the interventions. This study suggests that PSTs require significant preparation infused with practical experiences and examples in order to design a linguistically and conceptually rich lesson

International linkage of real interest rates: the case of East Asian countries

This paper examines linkage of real interest rates for a group of selected countries in East Asia. The countries under study include Japan, Korea, Singapore, Malaysia and Thailand. The long run relationship is tested and estimated using the conitegration analysis. We also have conducted the impulse response analysis based on unrestricted vector autoregression, using the bias-corrected wild bootstrap for statistical inference. Our results show that (1) there exists a long run equilibrium relationship, (2) there are interesting short run dynamic interactions, in which Singapore, Malaysia and Thailand play the role of equilibrating factorFinancial linkage; Real interest rate parity; Cointegration analysis; Wild bootstrap

Two-dimensional Rydberg gases and the quantum hard squares model

We study a two-dimensional lattice gas of atoms that are photo-excited to high-lying Rydberg states in which they interact via the van-der-Waals interaction. We explore the regime of dominant nearest neighbor interaction where this system is intimately connected to a quantum version of Baxter's hard squares model. We show that the strongly correlated ground state of the Rydberg gas can be analytically described by a projected entangled pair state that constitutes the ground state of the quantum hard squares model. This correspondence allows us to identify a first order phase boundary where the Rydberg gas undergoes a transition from a disordered (liquid) phase to an ordered (solid) phase

Rate of Convergence in Nonlinear Hartree Dynamics with Factorized Initial Data

The mean field dynamics of an $N$-particle weekly interacting Boson system can be described by the nonlinear Hartree equation. In this paper, we present estimates on the 1/N rate of convergence of many-body Schr\"{o}dinger dynamics to the one-body nonlinear Hartree dynamics with factorized initial data with two-body interaction potential $V$ in $L^3 (\mathbb{R}^3)+ L^{\infty} (\mathbb{R}^3)$.Comment: AMS LaTex, 21 page

Do Social Justice Contexts Matter in Mathematical Modeling?: Modeling Problem Analysis

Since the Common Core State Standards for Mathematics (CCSSM; NGA Center for Best Practices & CCSSO, 2010) include modeling as one of the eight Standards for Mathematical Practices for all grades but also as important conceptual category in high school mathematics, there have been a spotlight on mathematical modeling and demand for teachers to deliberately integrate modeling tasks in mathematics classrooms. One of the efforts to integrate modeling in mathematical curricula is including modeling problems in textbooks. It is necessary to examine if these attempts are adequately made in mathematical curricula (Meyer, 2015)

Teacher Perspectives on Mathematics Education of Language Learners: Adapting ELL Education Models

Teachers in Korea have recently confronted new challenges as the population of linguistically and culturally diverse students increases. Ethnically diverse students as well as Korea-born students returning from long residences in foreign countries have great difficulties orienting themselves within Korean schools due to lack of Korean language proficiency and cultural differences. We named this student group as Korean language learners (KLLs) and investigated teacher perspectives on effective mathematics pedagogy for KLLs. Using two educational models for English language learners (ELLs)—Cummins’ Quadrant Model and the Sheltered Instruction Observation Protocol (SIOP) Model—we examined survey results of a small group of elementary teachers in South Korea in terms of effectiveness and feasibility of the ELL models

Preservice Teacher Learning to Help ELS Understand Mathematical Problems

There is a common belief that teachers do not need to differentiate their instruction for English Learners (ELs) and that helping ELs adjust in school culture is not a teacher’s responsbility (Walker, Shafer, & Liams, 2004). This belief is due to their lack of proper training to teach ELs, as statistics show only 13% of teachers are adequately prepared to teach ELs while more than 40% of teachers have ELs in their classrooms (NCES, 2002). Responding to the great need for an adequate teacher preparation for EL in mathematics education, this study was designed to investigate preservice teacher (PSTs) learning to help ELs understand mathematics