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

Research and Utilization of Windmill

The thesis researches the characteristics of the wind power, the operation and design of the windmill. The design part involves the strength calculation and the method of placing and fixing the windmill on a high building. The methods applied in the thesis include preliminary study of the wind power, functional specification of the wind mill and technical specification of the design of wind mill. The environment aspect should be considered more when designing something as an engineer in the future

Ligand Path: A Software Tool for Mapping Dynamic Ligand Migration Channel Networks

AbstractProteins are essential compositions of the living organisms and involved in the processes of different life events. Basically proteins are like amazing tiny bio-machines performing the functions in a stable and predictable manner and understanding the underline mechanisms can facilitate the pharmaceutical development. However, protein functions are not carried in a static style, so experimental observations of these dynamic movements of the drugs inside the proteins are difficult, so computational methods have an important and irreplaceable role.We developed a software tool called LigandPath for mapping the ligand migration channels in a constantly moving protein and this software can function with CADD (Computer aided drug design) software to map the possible migration pathways of candidate drugs inside a protein. Traditionally, biologists use MD (Molecular Dynamics) simulation to locate the ligand migration channels, but it takes long time for them to observe the complete migration paths. In order to overcome the limitations of the trajectory-based MD simulation, we adopt a computational method inspired from robotic motion planning called DyME (Dynamic Map Ensemble) and we develop the software tool LigandPath based on DyME. The software tool has already been successfully applied to map the potential migration channels of drugs candidates of three proteins, PPAR (peroxisome proliferator-activated receptors), UROD (uroporphyrinogen decarboxylase) and Sirt1 (silent information regulator 1) complexes in three publications

Experimental Study on Match for Indoor and Outdoor Heat Exchanger of Residential Air-conditioner

In this study, the effects of indoor unit heat transfer area and air flow rate and outdoor unit air flow rate on the system performance of residential air-conditioner were experimentally investigated under rated cooling and heating conditions. The experimental results showed that the system cooling capacity, EER, heating capacity and COP all had evident variation with indoor unit heat transfer area and air flow rate and out unit air flow rate, which predicated that there was a proper match range for indoor unit and outdoor unit to make the system overall performance best. The increase of indoor unit heat transfer area and air flow rate significantly improved system cooling and heating performances especially for the smaller heat transfer area indoor unit, and the improvement was more obvious for heating performance. The heat transfer area ratio of indoor unit and outdoor unit was smaller, the indoor unit air flow rate should be designed as higher air velocity, but that should not be higher than 1.2m/s. In addition, with the specified outdoor unit in this study, the matched heat transfer area of indoor unit should not be too high or too low, and the optimal heat transfer area ratio of indoor and outdoor unit was between 0.33 and 0.37, which was better to choose the smaller value for higher indoor unit air flow rate. The increase of outdoor unit air flow rate also was advantageous for improving system cooling and heating performances especially for system EER and COP, but excessive higher air flow rate can cause the degradation of the system performance. The proposed outdoor unit designed air velocity should not be higher than 1.6m/s

Experimental Investigation of the Refrigerant Flow Distribution Characteristic of Heat Exchangers on the Residential Heat Pump Air Conditioner System Performance

In this study, the refrigerant flow distribution characteristic of fin-and-tube heat exchanger used as outdoor and indoor heat exchanger of a residential heat pump air-conditioner was experimentally studied and analyzed. The outdoor heat exchanger included “n shape†1 -circuit, 2-circuit and 3-circuit arrangements, and the indoor heat exchanger was only “n shape†2–ciucuit arrangement. It showed that the refrigerant flow distribution of both outdoor and indoor heat exchanger as evaporator would give much more system performance change of the residential heat pump air-conditioner than that as condenser. The refrigerant flow distribution characteristic can be expressed with the difference value of each circuit exit superheat as evaporator. The maximum difference value with little effect on system performance had been obtained both under cooling mode and heating mode. The maximum difference value was nearly the same at various test conditions and can be considered as 3℃. According to the experimental results, the system performance under heating mode especially for rated heating mode had more sensitive with refrigerant flow distribution characteristic than that under cooling mode, therefore the adjustment of refrigerant distribution characteristic of both the outdoor and indoor heat exchanger should mainly base on the rated heating mode

Study of R161 Refrigerant for Residential Air-conditioning Applications

In order to investigate the feasibility of R161 applied in residential air conditioner, the thermodynamic performance and comprehensive theoretical thermodynamic cycle of R161, R22 and R290 under various air-conditioner operating condition were carried out. Further more, the cooling and heating performance of R161 and R22 under various operating condition was investigated experimentally in a 3.5kW residential heat pump air conditioner. Property and thermodynamic cycle comparison showed that R161 has better thermodynamic performance than R290, the rated cooling and heating capacity is lower than R22 but higher than R290, the rated cooling and heating COP is higher than both R22 and R290. The experimental rated cooling capacity reduced 7.6% and rated cooling EER increased 6.1%, rated heating capacity reduced 6.8% and rated heating COP increased 4.7%, refrigerant optimized charge reduced 43% compared to R22 system, theoretical and experimental test revealed that R161 has lower discharge temperature than R22 system