Fermionic-mode entanglement in non-Markovian environment

We evaluate the non-Markovian effects on the entanglement dynamics of a fermionic system interacting with two dissipative vacuum reservoirs. The exact solution of density matrix is derived by utilizing the Feynman–Vernon influence functional theory in the fermionic coherent state representation and the Grassmann calculus, which are valid for both the fermionic and bosonic baths, and their difference lies in the dependence of the parity of the initial states. The fermionic entanglement dynamics is presented by adding an additional restriction to the density matrix known as the superselection rules. Our analysis shows that the usual decoherence suppression schemes implemented in qubits systems can also be achieved for systems of identical fermions, and the initial state proves its importance in the evolution of fermionic entanglement. Our results provide a potential way to decoherence controlling of identical fermions.     

一个非平凡的Calabi-Yau DG代数

证明例1中的DG代数不仅是Koszul,同调光滑DG代数,而且还是一个Calabi-Yau DG代数.该例子说明一个Calabi-Yau DG代数的同调分次代数不一定具有Calabi-Yau性质,甚至可能不是同调光滑的;另外,该例子还说明一个Calabi-Yau DG代数忘掉微分后得到的分次代数不一定是分次Calabi-Yau代数.     

SUBSTITUTED 4,5-DIOXO-1,3-DIAZA-2λ3,4λ4-DIPHOSPHOLANE AND RELATED COMPOUNDS

Abstract

Cyclization of 1 with 2 yielded the title compound 3, which was transformed into the corresponding 1,3,2,4-diazadiphospholanes 4 and 5 by using DMSO or sulfur respectively. The addition reaction of 3 with butanedione gave 3,4-di-oxo-1-phenyl-2,5-diaza-6,9-dioxa-1λ⁵,3λ⁴-diphosphaspiro[4,4]nonane 6. The structures of 3, 4 and 5 were confirmed by elemental analysis, IR, NMR and GC-MS. Although 6 could not be isolated in pure form because of its rapid decomposition, the ₃₁P NMR data indicated its existence. It was found that there were cis- and trans-isomers in 3, 4, 5 and 6.     

Preparation and Characterization of Linear and Miktoarm Star Side-Chain Liquid Crystalline block Copolymers with p-Methoxyazobenzene Moieties via a Combination of ATRP and ROP

One linear and two miktoarm star side-chain liquid crystalline (LC) block copolymers with p-methoxyazobenzene moieties were prepared by a combination of ring-opening polymerization (ROP) and atom transfer radical polymerization (ATRP) techniques. First, ROPs of ε -caprolactone (ε -CL) were carried out catalyzed by Sn(Oct)₂ using three multifunctional initiators, hydroxyethyl 2-bromoisobutyrate (AB type), 3-hydroxy-2-(hydroxymethyl)-2-methylpropyl 2-bromo-2-methylpropanoate (A₂B type) and 2,2-bis(hydroxymethyl)propane-1,3-diyl bis(2-bromo-2-methylpropanoate) (A₂B₂ type), at 110°C in toluene, respectively. Second, the previously obtained poly(ε -caprolactone)s (PCLs) with bromines functionalities were used as the macroinitiators to conduct ATRP of 6-(4-methoxy-4-oxy-azobenzene) hexyl methacrylate (MMAZO) with CuBr/PMDETA as the catalyst systems at 85°C in anisole to prepare the linear and miktoarm side-chain LC block copolymers (PCL-b-PMMAZO, (PCL)₂-(PMMAZO) and (PCL)₂-(PMMAZO)₂). The produced polymers were well-controlled with the controlled molecular weights and the relatively narrow molecular weight distributions (M _w/M _n ≤ 1.35). The structures of the obtained polymers were all characterized by NMR, FT-IR and GPC analysis. Furthermore, the LC properties of the linear and miktoarm star block copolymers were also investigated by differential scanning calorimetry (DSC) and thermal polarized optical microscopy (POM).     

Synthesis of Main‐Chain Liquid‐Crystalline Polyesters Containing Diphenyl Mesogens by Chemo‐Enzymatic Route †

Main‐chain thermotropic liquid‐crystalline polyesters containing rigid biphenyl mesogens and flexible spacers were synthesized by chemo‐enzymatic route. The enzyme‐catalyzed polymerization showed high regio‐ and chemo‐ selectivity, and is environmentally friendly. The resulting polyesters were characterized with ¹H‐NMR, ¹³C‐NMR, gel permeation chromatography (GPC), differential scanning calorimetry (DSC), and polarized light optical microscopy (POM).     

A Tensile Strain Hardening Test Indicator of Environmental Stress Cracking Resistance

Environmental stress cracking resistance (ESCR) is an important indicator of performance for high density polyethylene (HDPE) in structural and polymer pipe applications. The commonly used test for determining ESCR of HDPE can be time consuming and rather imprecise. A tensile strain hardening test was recently proposed to offer a faster way to characterize ESCR of polyethylene. In this paper, a practical approach is adopted whereby the test is extended to room temperature and shown to relate reliably to the ESCR of HDPE. Several HDPE resins (including pipe‐grade resins) are analyzed at strain rates of 0.5 mm/min and 7 mm/min to compare the effect of strain rate. Comparisons between the conventional ESCR test method and the strain hardening test show that strain hardening can be used to rank ESCR of HDPE in a reliable fashion. In our study the more direct measure of “hardening stiffness” is used to compare resins instead of strain hardening modulus. Because no true stress‐strain measurement is needed, this is a much simpler test method than other methods previously suggested. In addition, the use of the natural drawing ratio (NDR) as ESCR ranking indicator is examined. Results show that NDR can also be employed as a strain rate‐independent indicator of ESCR of HDPE. The test proposed herein is practical, simple and precise, and hence a more reliable indicator of ESCR performance of HDPE.