Non-Noether conserved quantity constructed by using form invariance for Birkhoffian system

Based on the invariance of Birkhoffian equations under the infinitesimal transformations of groups, the definition and the criterion of a form invariance for a Birkhoffian system are established. The condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced by relyingon the total time derivative along the trajectory of the equations, and two corollaries in special cases are presented. An example is finally given to illustrate the application of the results.     

Information Entropy Squeezing for a Atom in Mode-Mode Competition System

The entropy squeezing properties for a two-level atom interacting with a two-mode field via two different competing transitions are investigated from a quantum information point of view. The influences of the initial state of the system and the relative coupling strength between the atom and the field on the atomic information entropy squeezing are discussed. Our results show that the squeezed direction and the frequency of the information entropy squeezing can be controlled by choosing the phase of the atom dipole and the relative competing strength of atom-field, respectively. We find that, under the same condition, no atomic variance squeezing is predicted from the HUR while optimal entropy squeezing is obtained from the EUR, so the quantum information entropy is a remarkable precision measure for the atomic squeezing in the considered system.     

Husimi Operator for Describing Probability Distribution of Electron States in Uniform Magnetic Field Studied by Virtue of Entangled State Representation

For the first time we introduce an operator Δ _h (γ,ε;κ) for studying Husimi distribution function in phase space (γ,ε) for electron’s states in uniform magnetic field, where κ is the Gaussian spatial width parameter. The marginal distributions of the Husimi function are Gaussian-broadened version of the Wigner marginal distributions. Using the Wigner operator in the entangled state 〈λ | representation we find that Δ _h (γ,ε;κ) is just a pure squeezed coherent state density operator | γ,ε〉 _{κ κ} 〈γ,ε |, which brings much convenience for studying Husimi distribution, so we name Δ _h (γ,ε;κ) the Husimi operator. We then derive Husimi operator’s normally ordered form that provides us with an operator version to examine various properties of the Husimi distribution. Work supported by the National Natural Science Foundation under the grant: 10775097.     

Up-conversion white light of Tm/Er/Yb tri-doped CaF2 phosphors

Tm³⁺/Er³⁺/Yb³⁺ tri-doped CaF₂ phosphors were synthesized using a hydrothermal method. The phosphors were characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), and up-conversion (UC) emission spectra. After annealing, the phosphors emitted white light under a 980 nm continuous wave diode laser (CW LD 2 W) excitation. As the excitation power density changed in the range of 20-260 W/cm², the chromaticity coordinates of the UC light of the phosphor Ca_0.885Tm_0.005Er_0.01Yb_0.1F₂ fell well in the white region of the 1931 CIE diagram. For the proportion of red, green and blue (RGB) in white light is strict, key factors for achieving UC white light, such as host materials, rare earth ions doping concentrations, annealing temperatures, as well as the excitation power densities, were investigated and discussed.     

Undercooling and Unidirectional Solidification of CuNi Alloy Melts

Cylinder-shaped CusoNi20 alloy melt is undercooled and solidified by the combination of the electromagnetic levitation technique and the flux treatment method. Nearly constant temperature gradient of 8-10 K/cm is realized for the cylindrical melts with differen~ undercooling levels at the bottom ends. The experimental results reveal that with the increase of the undercoo]ing of the melts from 35 to 220 K, the microstructures undergo transition from coarse dendrites to granular grains, unidirectional dendrites, and finally to equiaxed grains.     

Mechanistic Insights into the Synthesis of Fully Condensed Polyhedral Octaphenylsilsesquioxane

A comprehensive study on the efficient one‐pot synthesis of polyhedral octaphenylsilsesquioxane (OPS) is reported via the hydrolytic condensation of phenyltrimethoxysilane (PTMS) in the presence of basic catalyst to investigate the specific synthesis mechanism. The synthetic reactions are monitored with real time infrared (RTIR) spectroscopy. Then RTIR coupled with ²⁹Si nuclear magnetic resonance spectroscopy (NMR) and matrix‐assisted laser desorption/ionization time of flight mass spectrometry (MALDI‐TOF‐MS) are used to monitor the reactions and identify the intermediary species during the reaction. The rapid hydrolysis of PTMS is detected by RTIR. Contrary to previous reports, the ladder‐like structured species are identified as intermediates during the reaction process. It is suggested that formation of caged T₈ OPS is realized through the chain break and rearrangement of the ladder‐like phenyltrimethoxysilanes. Accordingly, a scheme from hydrolysis of the PTMS to formation of the OPS is provided.     

Progress of organic magnetic materials

Over the past years, the development of magnetic materials has been intensively explored, both for fundamental research and technological applications. Particularly, several materials with large magnetoresistance effect have received significant interest.In this study, we provide an analysis of the progress of organic magnetic materials and organic magnetoelectric complexes, thus paving the way for the understanding of organic magnetism and magnetoelectric coupling mechanisms. In addition, this analysis provides us a critical guide for future organic magnetic material design and fabrication.