Entanglement entropy and entanglement spectrum of the Kitaev model

In this paper, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S=S_G+S_F, with S_F the entanglement entropy of a free Majorana fermion system and S_G that of a Z_2 gauge field. The Z_2 gauge field part contributes to the universal "topological entanglement entropy" of the ground state while the fermion part is responsible for the non-local entanglement carried by the Z_2 vortices (visons) in the non-Abelian phase. Our result also enables the calculation of the entire entanglement spectrum and the more general Renyi entropy of the Kitaev model. Based on our results we propose a new quantity to characterize topologically ordered states--the capacity of entanglement, which can distinguish the states with and without topologically protected gapless entanglement spectrum.Comment: 4.0 pages + supplementary material, published version in Phys. Rev. Let

Study on the extraction method of transverse open crack’s information

For the fault rotor – bearing system caused by transverse open crack. The dynamic model of crack rotor system is established by the crack compliance coefficient matrix which is derived from the stress intensity factor and strain energy density function. The stiffness matrix of rotor system which contains transverse crack faults is different from the health rotor. So the surplus dynamics equation of cracked rotor system can be deduced by comparing the dynamics equations of the crack fault and health rotor system, which is on the basis of getting the compliance coefficient matrix. Furthermore, the information of open crack’s location and crack’s depth can be extracted from the vibration signal by analyzing force condition on both ends of the shaft segment where crack exist and combining with the residual dynamic equation. The extraction method for crack information only needs to collect the vibration signals of the three different node positions under two different speeds. Finally, the feasibility of the method can be verified with simulation and experiment

Volume confinement induced microstructural transitions and property enhancements of supramolecular soft materials

The rheological properties of supramolecular soft functional materials are determined by the networks within the materials. This research reveals for the first time that the volume confinement during the formation of supramolecular soft functional materials will exert a significant impact on the rheological properties of the materials. A class of small molecular organogels formed by the gelation of N-lauroyl-L-glutamic acid din-butylamide (GP-1) in ethylene glycol (EG) and propylene glycol (PG) solutions were adopted as model systems for this study. It follows that within a confined space, the elasticity of the gel can be enhanced more than 15 times compared with those under un-restricted conditions. According to our optical microscopy observations and rheological measurements, this drastic enhancement is caused by the structural transition from a multi-domain network system to a single network system once the average size of the fiber network of a given material reaches the lowest dimension of the system. The understanding acquired from this work will provide a novel strategy to manipulate the network structure of soft materials, and exert a direct impact on the micro-engineering of such supramolecular materials in micro and nano scales

Determination of metabolites of phloretin in rats using UHPLC-LTQ-Orbitrap mass spectrometry

Purpose: To study the metabolites of phloretin in vivo using ultra-high performance liquid chromatography linear ion trap-Orbitrap mass spectrometry (UHPLC-LTQ-Orbitrap). Methods: After administration of phloretin (50 mg/kg; oral route) to six rats, blood samples were taken from each animal. Each sample was then subjected to solid-phase extraction to prepare it for chromatographic/spectroscopic analysis. Finally, each sample was analyzed using UHPLC-LTQOrbitrap with a negative-mode electrospray ionization source. Results: Based on mass measurements, chromatographic retention times, and MS2 fragmentation ions, we detected and identified phloretin and 16 metabolites of the drug in vivo in rats. Metabolic reactions of phloretin included glucosylation and glucuronide conjugation, diglucuronide conjugation, glucosylation and sulfate conjugation, sulfate conjugation, glucuronide conjugation, and glucosylation and hydroxylation. Conclusion: The findings provide a better understanding of phloretin metabolism and metabolites, and new information about their effective forms, pharmacological actions, metabolic fate, and toxic actions in vivo