Momentum polarization: an entanglement measure of topological spin and chiral central charge

Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin $\theta_a=2\pi h_a$ is an important property of a topological quasi-particle, which is the Berry phase obtained in the adiabatic self-rotation of the quasi-particle by $2\pi$. For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge $c$. In this paper we propose a new approach to compute the topological spin and chiral central charge in lattice models by defining a new quantity named as the momentum polarization. Momentum polarization is defined on the cylinder geometry as a universal subleading term in the average value of a "partial translation operator". We show that the momentum polarization is a quantum entanglement property which can be computed from the reduced density matrix, and our analytic derivation based on edge conformal field theory shows that the momentum polarization measures the combination $h_a-\frac{c}{24}$ of topological spin and central charge. Numerical results are obtained for two example systems, the non-Abelian phase of the honeycomb lattice Kitaev model, and the $\nu=1/2$ Laughlin state of a fractional Chern insulator described by a variational Monte Carlo wavefunction. The numerical results verifies the analytic formula with high accuracy, and further suggests that this result remains robust even when the edge states cannot be described by a conformal field theory. Our result provides a new efficient approach to characterize and identify topological states of matter from finite size numerics.Comment: 13 pages, 8 figure

Turbulence control by developing a spiral wave with a periodic signal injection in the complex Ginzburg-Landau equation

Turbulence control in the two-dimensional complex Ginzburg-Landau equation is investigated. A new approach is proposed for the control purpose. In the presence of a small spiral wave seed initiation, a fully developed turbulence can be completely annihilated by injecting a single periodic signal to a small fixed space area around the spiral wave tip. The control is achieved in a parameter region where the spiral wave of the uncontrolled system is absolutely unstable. The robustness, convenience and high control efficiency of this method is emphasized, and the mechanism underlying these practical advantages are intuitively understood.Comment: 12 pages, figures can be found in the following journa

AGRICULTURAL TECHNOLOGY EXTENSION SYSTEM IN CHINA： CURRENT SITUATION AND REFORM DIRECTION

This paper presents the evolution of China’s Agricultural Technology Extension (ATE) System since its inception in 1920s. China’s ATE system has gone through 5 stages before the current system was formed. It evolved from basic-level extension network in 1950s, mid-level extension organizations in 1960s，gradually into nation-wide extension system in 1980s. The participative extension network was reconstructed during “the Cultural Revolution” period. The reform of extension system of China has been intensified since 1992 and the five-level Agricultural Technology Extension organizations were basically established. Compared with those previous ones, the current extension system is much better in its setting hierarchy, functions and extension efficiency. However, at present, China’s ATE system is also facing such problems as investment deficiency, low-quality and redundant extension team, failure to meet the market needs and government domination, etc. Based on these problems, some reform directions and measures to perfect China’s ATE system are proposed. Key words: evolution, China’s Agricultural Extension Technology System, history, status quo, refor

Data on Breastfeeding and State Policies in the United States

Breastfeeding is critically important to maternal and child health in the United States. Examining the relationship between breastfeeding outcomes and state policies requires multidisciplinary efforts to link data from various sources. This article describes an integrated dataset that was used to understand the relationship between participation in a nutrition assistance program and low-income children\u27s breastfeeding outcomes [1]. This dataset merged public health information from the National Immunization Surveys Data from 2006 to 2016 and matching state policy data from the Correlates of State Policy Project (CSPP), the U.S. Department of Agriculture/Economic Research Services (USDA/ERS) Supplemental Nutrition Assistance Program (SNAP) Policy Index, the U.S. Bureau of Labor Statistics (BLS), Centers for Medicare & Medicaid Services (CMS), and the Census Bureau. The integrated dataset compiles variables in breastfeeding outcome, child\u27s and mother\u27s socio-demographic characteristics, and state-level policy measures, including SNAP participation rates, SNAP policy indices, unemployment rates, and Children\u27s Health Insurance Program (CHIP) enrollment rates. This multidisciplinary dataset included information on a total of 219,904 children with 98 variables

SPECT Molecular Imaging in Parkinson's Disease

Parkinson's disease (PD) is a common disorder, and the diagnosis of Parkinson's disease is clinical and relies on the presence of characteristic motor symptoms. The accuracy of the clinical diagnosis of PD is still limited. Functional neuroimaging using SPECT technique is helpful in patients with first signs of parkinsonism. The changes detected may reflect the disease process itself and/or compensatory responses to the disease, or they may arise in association with disease- and/or treatment-related complications. This paper addresses the value of SPECT in early differential diagnosis of PD and its potential as a sensitive tool to assess the pathophysiology and progression, as well as the therapeutic efficacy of PD