Quantum Spin Dynamics with Pairwise-Tunable, Long-Range Interactions

We present a platform for the simulation of quantum magnetism with full control of interactions between pairs of spins at arbitrary distances in one- and two-dimensional lattices. In our scheme, two internal atomic states represent a pseudo-spin for atoms trapped within a photonic crystal waveguide (PCW). With the atomic transition frequency aligned inside a band gap of the PCW, virtual photons mediate coherent spin-spin interactions between lattice sites. To obtain full control of interaction coefficients at arbitrary atom-atom separations, ground-state energy shifts are introduced as a function of distance across the PCW. In conjunction with auxiliary pump fields, spin-exchange versus atom-atom separation can be engineered with arbitrary magnitude and phase, and arranged to introduce non-trivial Berry phases in the spin lattice, thus opening new avenues for realizing novel topological spin models. We illustrate the broad applicability of our scheme by explicit construction for several well known spin models.Comment: 18 pages, 10 figure

Defining teachers’ professional development needs:a study of implementing Marine Educator Training Course in Taiwan

Abstract. This thesis focuses on understanding teachers’ professional development needs after attending the Marine Educators Training Course in Taiwan from teachers’ perspectives. Taiwan started to implement Marine Education in 2008 after the White Paper on Marine Education Policy was released by the Ministry of Education, R.O.C. Teachers at all school levels were expected to integrate and teach marine-related topics in various fields of the 12-year basic education. Therefore, Taiwan Marine Education Center (TMEC) conducted an official Marine Educator Training Course to enhance teachers’ marine knowledge and teaching skills since 2017 to solve the dilemmas of implementing Marine Education discovered by the Ministry of Education, R.O.C. The conceptual frameworks of the thesis consist of teachers’ Marine Science Content Knowledge, Technological Pedagogical Content Knowledge (TPACK), teacher professional needs, Ocean Literacy (OL), and inspiration from UNESCO and SDGs. For this study, all the conceptual concepts are discussed under teacher professional development as the main fundamental concept. To clarify the conceptual framework of teachers’ needs for Marine Education in Taiwan, these five concepts were considered and related in implementing Marine Education for teachers. This is a qualitative research study involving an analysis of 51 responders among 173 participants of the Marine Educator Training Course from 2017 to 2019 in Taiwan. This study focused on understanding the teachers’ professional development needs that are still required for implementing Marine Education in the classroom after attending this training course. This study aimed to analyze the teachers’ answers to this specific open question was collected by an e-questionnaire. The methodology of this study used Qualitative Content Analysis (QCA). This study indicated that teachers in different school levels have different demand levels, and these demands could be divided into three areas. First, for elementary and junior high school teachers, they are the majority groups needing the support of Marine Educational TPACK compared to the other two groups. Second, the possible potential for the sixth principle of Ocean Literacy. Because the teacher lacks official textbooks and teaching materials in Marine Education. Third, the importance of school internal support. This internal support helps teachers to reduce their stressed and inexperienced feelings when implementing Marine Education. Simultaneously, teachers feel valued and acknowledged by the support from peers and administrations within schools. This study aims to bring insight from teachers’ perspectives and point out what the teachers’ professional development needs should have for marine education teachers in Taiwan. The observations of this study could be a potential example of Education for Sustainable Development for teacher training in basic education

Quantum many-body models with cold atoms coupled to photonic crystals

Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, as atoms are nominally neutral point particles, this limits the types of interactions that can be produced. We propose to use the powerful new platform of cold atoms trapped near nanophotonic systems to extend these limits, enabling a novel quantum material in which atomic spin degrees of freedom, motion, and photons strongly couple over long distances. In this system, an atom trapped near a photonic crystal seeds a localized, tunable cavity mode around the atomic position. We find that this effective cavity facilitates interactions with other atoms within the cavity length, in a way that can be made robust against realistic imperfections. Finally, we show that such phenomena should be accessible using one-dimensional photonic crystal waveguides in which coupling to atoms has already been experimentally demonstrated

Interacting Business Cycle Fluctuations: A Two-Country Model

In this paper, we develop a model of business cycle fluctuations between two interacting open economies within the disequilibrium or non-market clearing paradigm. We analyze the main feedback mechanisms (Keynes, Mundell, Rose and Dornbusch) driving the dynamics and the conflict between their stabilizing and destabilizing tendencies and how these depend on certain key speeds of adjustment in the real and foreign exchange sectors. We explore numerically a variety of situations of interacting price cycles in the two countries, where the steady state is locally repelling, but where the overall dynamics are bounded in an economically meaningful domain by assuming downward money wage rigidity

A Study of Anyon Statistics by Breit Hamiltonian Formalism

We study the anyon statistics of a $2 + 1$ dimensional Maxwell-Chern-Simons (MCS) gauge theory by using a systemmetic metheod, the Breit Hamiltonian formalism.Comment: 25 pages, LATE

The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach

ABSTRACT. This paper considers the dynamics for interest rate processes within a multi-factor Heath, Jarrow and Morton (1992) specification. Despite the flexibility of and the notable advances in theoretical research about the HJM models, the number of empirical studies is still inadequate. This paucity is principally because of the difficulties in estimating models in this class, which are not only high-dimensional, but also nonlinear and involve latent state variables. This paper treats the estimation of a fairly broad class of HJM models as a nonlinear filtering problem, and adopts the local linearization filter of Jimenez and Ozaki (2003), which is known to have some desirable statistical and numerical features, to estimate the model via the maximum likelihood method. The estimator is then applied to the interbank offered-rates of the U.S, U.K, Australian and Japanese markets. The two-factor model, with the factors being the level and the slope effect, is found to be a reasonable choice for all of the markets. However, the contribution of each factor towards overall variability of the interest rates and the financial reward each factor claims differ considerably from one market to another

The Evolution of Diffuse Radio Sources in Galaxy Clusters

We investigate the evolution and number distribution of radio halos in galaxy clusters. Without re-acceleration or regeneration, the relativistic electrons responsible for the diffuse radio emission will lose their energy via inverse-Compton and synchrotron losses in a rather short time, and radio halos will have lifetimes $\sim$ 0.1 Gyr. Radio halos could last for $\sim$ Gyr if a significant level of re-acceleration is involved. The lifetimes of radio halos would be comparable with the cosmological time if the radio-emitting electrons are mainly the secondary electrons generated by pion decay following proton-proton collisions between cosmic-ray protons and the thermal intra-cluster medium within the galaxy clusters. Adopting both observational and theoretical constraints for the formation of radio halos, we calculate the formation rates and the comoving number density of radio halos in the hierarchical clustering scheme. Comparing with observations, we find that the lifetimes of radio halos are $\sim$ Gyr. Our results indicate that a significant level of re-acceleration is necessary for the observed radio halos and the secondary electrons may not be a dominant origin for radio halos.Comment: 22 pages, 6 figures, ApJ, in press (v2:Corrected typos.

An analysis of the cobweb model with boundedly rational heterogeneous producers

This paper considers the traditional cobweb model with heterogenous risk averse producers whose supply functions involve their estimates of the conditional mean and variance of the future price. The producers seek to learn these quantities by applying geometric decay processes (GDP) to past prices. The heterogeneity manifests itself in the lag lengths and memory parameters applied to past prices as well as in risk aversion coefficients. We find that each dimension of heterogeneity changes/enriches the cobweb dynamics with respect to the case of homogeneous producers. © 2006 Elsevier B.V. All rights reserved