Exponential Attractor for a Class of Nonclassical Diusion Equation

In this paper, we consider the asymptotic behavior of solutions for a class of nonclassical diffusion equation. We show the squeezing property and the existence of exponential attractor for this equation. We also make the estimates on its fractal dimension and exponential attraction.     

非经典多重键

在难以形成经典多重键的重原子（第三周期以下）之间可以形成一种非经典多重键。由于构成双键的两部分（即两个分子片）的基态分别是单线态,这种电子结构导致非经典双键由两个配位键构成,非经典三键则是在此基础上再加上一个π键。这种多重键的强度和键级较经典多重键为低。与两个配位键的电子结构相对应,含有非经典多重键的分子具有反式弯曲的几何构型。     

Linear amplifier via the displaced Fock states superposition

The linear amplifier with the superposition of displaced Fock states (DFS’s) as an input field is discussed. The s-parameterized characteristic function (CF) of linear amplifier for the superposition of two DFS’s is considered. Several quantum statistical expectation values for the output of linear amplifier are evaluated once the time dependent CF has been computed. The Glauber secondorder coherence function is calculated. The squeezing properties of the output field are studied. The s-ordered quasiprobability distribution function (QDF) for the output of linear amplifier driven by DFS’s superposition is investigated. The phase properties of the superposition of DFS’s are studied. The s-parameterized phase distribution, obtained by integrating the s-parameterized QDF over radial variable is illustrated.     

Statistical properties of the output of linear amplifier with superpositions of squeezed displaced Fock states as an input state

The s-parameterized characteristic function for the output field with the superposition of squeezed displaced Fock states (SDFS's) as input field is given. The s-ordered distribution functions for the output field with superposition of SDFS's as input state are investigated. Various moments are calculated by using the s-ordered characteristic function for that field. The Glauber second-order coherence function is calculated. The quadrature squeezing for the output field are discussed. Some Quasiprobability distribution functions of the output fields are plotted as functions of the interaction time. The quadrature squeezing for the output field are discussed. Received 30 September 1998     

Intramolecular Nicholas Reaction Enables the Stereoselective Synthesis of Strained Cyclooctynes

Cyclic products can be obtained through the intramolecular version of the Nicholas reaction, which requires having the nucleophile connected to the alkyne unit. Here, we report the synthesis of 1-oxa-3-cyclooctynes starting from commercially available (1R,3S)-camphoric acid. The strategy is based on the initial preparation of propargylic alcohols, complexation of the triple bond with Co₂(CO)₈, and treatment with BF₃·Et₂O to induce an intramolecular Nicholas reaction with the free hydroxyl group as nucleophile. Finally, oxidative deprotection of the alkyne afforded the cyclooctynes in good yields. Notably, large-sized R substituents at the chiral center connected to the O atom were oriented in such a way that steric interactions were minimized in the cyclization, allowing the formation of cyclooctynes exclusively with (R) configuration, in good agreement with theoretical predictions. Moreover, preliminary studies demonstrated that these cyclooctynes were reactive in the presence of azides yielding substituted triazoles.     

Superposition of two coherent states π out of phase with average photon number as relative phase

This paper discusses nonclassical features of the superposition of two coherent states π out of phase with each other and parameterized solely by amplitude α, that is, when the relative phase has a relationship with average photon number ∣α∣². In particular, it discusses oscillatory and sub-Poissonian photon statistics, degree of quadrature squeezing, and quasiprobability distribution functions. We examine that some nonclassical properties of these states are different from those of the even and odd coherent states.     

Minimum total noise is a measure of higher order squeezing

The possibility of observing higher order squeezing in different optical processes, such as six-wave mixing and four-wave mixing, has been studied and it is shown that amplitude squared squeezing appears in all these cases. It is also shown that the minimum total noise (T_min) of a higher order squeezed state, which is a measure of the total fluctuations in the field amplitude, always increases with the increase in depth of nonclassicality associated with higher order squeezing. Thus we can use T_min as an indirect measure of higher order squeezing.     

Pseudo-entanglement evaluated in noninertial frames

We study quantum discord, in addition to entanglement, of bipartite pseudo-entanglement in noninertial frames. It is shown that the entanglement degrades from its maximum value in a stationary frame to a minimum value in an infinite accelerating frame. There is a critical region found in which, for particular cases, entanglement of states vanishes for certain accelerations. The quantum discord of pseudo-entanglement decreases by increasing the acceleration. Also, for a physically inaccessible region, entanglement and nonclassical correlation are evaluated and shown to match the corresponding values of the physically accessible region for an infinite acceleration.     

Non-classical behavior in multimode and disordered transverse structures in OPO

We employ the Q-representation to study the non-classical correlations that are present from below to above-threshold in the degenerate optical parametric oscillator. Our study shows that such correlations are present just above threshold, in the regime in which stripe patterns are formed, but that they also persist further above threshold in the presence of spatially disordered structures. Received: 13 September 2002 / Received in final form: 11 November 2002 Published online 28 January 2003