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

Thermodynamics in the universe described by the emergence of the space and the energy balance relation

It has previously been shown that it is more general to describe the evolution of the universe based on the emergence of the space and the energy balance relation. Here we investigate the thermodynamic properties of the universe described by such a model. We show that the first law of thermodynamics and the generalized second law of thermodynamics (GSLT) are both satisfied and the weak energy condition are also fulfilled for two typical examples. Finally we examine the physical consistency for the present model.Comment: 9 pages, 2 figure

Applications Of Molecular And Quantum Mechanical Methods For Studying The Chemical Reactions Of Inorganic And Organic Systems

Computational studies can assist chemists to interpret experimental observations and to predict the properties and behaviors of molecules. The work presented in this dissertation applies different computational methods to study the molecular properties and reaction paths for various inorganic and organic systems. The second and third chapters discuss the force field development using “Gaussian Electrostatic Model (GEM)” and its amenability for use in the AMOEBA force field. The forth and fifth chapters discuss the density functional theory (DFT) studies of photodissociation behaviors for inorganic molecules. The sixth chapter explores the oxidation mechanisms of ascorbic acid and its antioxidant properties in bioorganic systems using a variety of quantum mechanic methods. The last chapter discuss the Born-Oppenheimer molecular dynamics simulation for the isomerization and fragmentation of allene cation in the strong laser field

A novel and environmentally friendly method for preserving and depilating sheepskin : comprehensive physical, biochemical and molecular analyses : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Biochemistry at Massey University, Manawatu, New Zealand

Figures are re-used with the publishers' permission.The first step of leather processing, depilation – in other words, removing hair from skins – accounts for one-third of the leather-making industrial waste due to the production of sulfide and alkaline water waste from the process. This study describes a method that preserves and depilates unwashed sheepskins using milk or milk by-products, including whey and permeate. It doesn’t require the use of harsh chemicals or temperature control, and results in skin that is ready to be tanned. In order to evaluate the products of this process, the depilated skin surface was evaluated not only by eye, but with scanning and transmission electron microscopy (SEM and TEM) which showed there was no apparent damage to the grain or fraying of the collagen bundles. The depilated skin was also processed to leather which was subjected to tear, tensile and shrinkage measurements which were shown to be almost identical to leathers made using the traditional process. Quantitative biochemical analyses, including collagen quantitation, collagen crosslink analysis and glycosaminoglycan (GAG) analysis of sheepskins depilated with this process showed no significant differences in both collagen, and collagen crosslink concentrations in contrast to the 10-fold increase seen in the GAG concentration. A quantitative proteomic analysis showed there was a higher retention of proteins found in the basement membrane of the skin, supporting the observation that permeate depilated skins were smoother than their sulfide depilated counterparts and produced leather with a superior surface. It also showed the loss of specific proteins around the hair follicle, hinting at a possible mechanism for depilation. To further investigate this a microbiological survey of the process was conducted. Traditional culturing methods were used to isolate and identify microorganisms present in the depilation solution after the wool had been removed. Two bacterial species (Lactococcus lactis and Lactobacillus plantarum) and two fungal species (Geotrichum candidum and Yarrowia lipolytica), were routinely identified, all of which are known to secrete a number of hydrolytic enzymes and antimicrobial compounds. This was followed by a metagenomic study of changes in the microbial community over the time course of the depilation. Although there were only 13 dominant bacterial genera identified during this study, the biggest change was a concomitant increase in the relative abundance of Lactococcus lactis that matched the decrease in Acinetobacter sp. by the end of the depilation treatment, controlling the proliferation of other putrefying organisms. In conclusion, this preliminary study has paved the way for the development of a depilation process that is kind to the environment, but more research is needed to investigate its potential use with other animal skins