Nonlinear evolution of quantum states in the adiabatic regime

We investigate adiabatic evolution of quantum states as governed by the nonlinear Schr?dinger equation and provide examples of applications with a nonlinear tunneling model for Bose-Einstein condensates. Our analysis not only spells out conditions for adiabatic evolution of eigenstates but also characterizes the motion of noneigenstates which cannot be obtained from the former in the absence of the superposition principle. We find that Aharonov-Anandan phases play the role of classical canonical actions and are conserved in the adiabatic evolution of noneigenstates.     

Synthesis of stable derivatives of c(62): the first nonclassical fullerene incorporating a four-membered ring

A rational synthetic approach to the first four-membered ring-containing derivatives of C(62) is reported. They were synthesized by an inverse electron demand Diels-Alder reaction of 3,6-diaryl-1,2,4,5-tetrazines with C(60) in o-dichlorobenzene, followed by visible light irradiation at reflux. The structure of these nonclassical fullerenes derivatives was determined by X-ray single-crystal diffraction.     

Laser-induced temperature jump electrochemistry on gold nanoparticle-coated electrodes

Laser-induced temperature jumps (LITJs) at gold nanoparticle-coated indium tin oxide (ITO) electrodes in contact with electrolyte solutions have been measured using temperature-sensitive redox probes and an infrared charge-coupled device. Upon irradiation with 532 nm light, interfacial temperature changes of ca. 20 degrees C were recorded for particle coverages of ca. 1 x 1010 cm-2. In the presence of a redox molecule, LITJ yields open-circuit photovoltages and photocurrents that are proportional to the number of particles on the surface. When ssDNA was used to chemisorb nanoparticles to the ITO surface, solution concentrations as low as 100 fM of target ssDNA-modified nanoparticles could be detected at the electrode surface.     

Diamond formation by reduction of carbon dioxide at low temperatures

This Communication reports a low-temperature diamond synthesis technique, in which diamonds (10-250 mum) can form at a temperature as low as 440 degrees C by reduction of dense CO2 with metallic Na. The X-ray diffraction pattern of a powder sample shows three reflection peaks, indexed with 111, 220, and 311, corresponding unambiguously to cubic diamond. The Raman spectrum of the product exhibits an intense first-order peak at 1332 cm-1, which is the characteristic signature of the cubic diamond, indicating the formation of well-crystallized diamond. Carbon dioxide is a nontoxic low-energy molecule, abundant on earth. This novel reduction method could allow studies of large-size diamond growth using CO2 as the carbon source.     

Layer-by-layer assembly of metal-mediated multiporphyrin arrays

Two types of multiporphyrin arrays, mediated by PdCl4(2-) complex ions at the air-water interface, were alternately transferred onto solid supports to form three-dimensional organized multilayers by a layer-by-layer method.     

Tetrahedral onsager crosses for solubility improvement and crystallization bypass

Pure organic molecules exhibiting a suitable concave rigid shape are expected to give porous glasses in the solid state. Such a feature opens new opportunities to avoid crystallization and to improve molecular solubility in relation to the high internal energy of these solid phases. To quantitatively explore the latter strategy, a series of rigid tetrahedral conjugated molecules nC and the corresponding models nR have been synthesized. Related to the present purpose, several properties have been investigated using UV absorption, steady-state fluorescence emission, differential scanning calorimetry, (1)H NMR translational self-diffusion, magic angle spinning (13)C NMR, and multiple-beam interferometry experiments. The present tetrahedral crosses are up to 8 orders of magnitude more soluble than the corresponding model compounds after normalization to the same molecular length. In addition, they give concentrated monomeric solutions that can be used to cover surfaces with homogeneous films whose thickness goes down to the nanometer range. Such attractive features make cross-like molecular architectures promising for many applications.     

Optical activity of microemulsion induced by electric field and its tunable behaviors

It has been shown that optical activity can occur in microemulsion under external electric field and rotation angle can also be tuned by the electric field. A set of microemulsions (water/Span80/transformer oil) with different water concentration were prepared and their optical activity was measured with the changes of applied electric field and θ, the angle between the electric vector of the incident linearly polarized light and the external electric field, using an automatic polarimeter. The experiments indicate that when none of the external electric field, water concentration and θ are zero, there is optical activity in microemulsions. For a given concentration, rotation angle ψ increases with electric field, and it firstly increases, passes through a maximum at C = C0,then monotonically decreases as C increases when electric field keeps constant. The relationship between the rotation angle and θ is also obtained. It is thought that the electric field-induced destroy of spatial symmetry of microemulsion is responsible for the optical activity of microemulsion.     

On the Upper Bound of Second Eigenvalues for Uniformly Elliptic Operators of any Orders

Abstract Let Ω R~m(m≥1)be a bounded domain with piecewise smooth boundary Ω.Let t and r bepositive integers with t>r+1. We consider the eigenvalue problems(1.1)and(12),and obtain Theorem 1and Theorem 2, which generalize the results in[1,2.5].