Energy-level statistics of model quantum systems: Universality and scaling in a lattice-point problem

We investigate the statistics of the numberN(R, S) of lattice pointsnZ ², in an annular domain (R, w)=(R+w)A\RA, whereR, w>0. HereA is a fixed convex set with smooth boundary andw is chosen so that the area of (R, w) isS. The statistics comes fromR being taken as random (with a smooth density) in some interval [c ₁ T,c ₂,T],c ₂>c ₁>0. We find that in the limitT the variance and distribution of N=N(R; S)–S depend strongly on howS grows withT. There is a saturation regimeS/T, asT, in which the fluctuations in N coming from the two boundaries of are independent. Then there is a scaling regime,S/Tz, 0<z<, in which the distribution depends onz in an almost periodic way going to a Gaussian asz0. The variance in this limit approachesz for genericA, but can be larger for degenerate cases. The former behavior is what one would expect from the Poisson limit of a distribution for annuli of finite area.     

Absence of absolutely continuous spectrum of Floquet operators

The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvalues _j of the unperturbed Hamiltonian grows as _j - _j-1 j and the multiplicity of _j grows asj with >0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough.     

CdS nanoclusters stabilized by thiolate ligands: A mini-review

One of the most exciting frontiers in materials chemistry in recent years is the optoelectronics of quantum-confined semiconductor nanoclusters. These nanoclusters are 10–200 A in diameter, and in this size regime exhibit extra-ordinarily interesting quantum mechanical effects. Cadmium sulfide is a popular semiconductor for these studies, and reviewed here is the synthesis and charac-terization of such CdS nanoclusters, with emphasis on how chemical control of the surface by thiolates influences product formation and properties. Also described are the syntheses and structures of true molecular clusters of CdS capped with thiolate ligands.     

Isolated square planar metal complexes of carbon

Based on the group theory analysis and quantum chemical calculations within the framework of SW X _α method (in relativistic approximation for core electrons and non-relativistic for valence ones), the existence possibility of square planar complexes [M₄C] and [M₄C]^2? (M = Al, Ga, In, Tl, Sc, and Y) in gas phase has been shown. The extraction of Kt₂[M₄C] square planar complexes of carbon in the crystal state is possible too. A high stability of these complexes, in comparison with usual tetrahedral, is achieved due to the formation of five-and four-center bonds (bonds M-M and M-C).     

Thermodynamics for Coulomb systems: A problem at vanishing particle densities

In this paper I combine techniques recently developed by Charles Fefferman with the well-known methods of Joel Lebowitz and Elliott Lieb to resolve some technical problems left unsettled by Lebowitz and Lieb's fundamental 1972 paper The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei.     

Equilibrium theory of two-dimensional simple liquids

Using the Wigner-Kirkwood expansion and bare Lennard-Jones (LJ) (12-6) potential, an effectiveLJ potential is derived, which includes the quantum effects through the expressions of the effective diameter∂(T, λ) and well-depth (T, λ). We use theWCA perturbation theory to calculate the free energy and pressure for theLJ and effectiveLJ potentials. Simple analytic expressions are given for the reference system and the first order correction calculated. The results are quite good at high density. The quantum effects on the free energy and pressure are also discussed.     

Preparation and properties of polymer and quantum dot composites

Quantum dots (QDs) were prepared in an organic system through a simple and low-cost wet chemistry method. Polymer beads with a diameter of 60–70 nm and specific functional groups were synthesized by a particular seeded emulsion polymerization technique. QDs were embedded in the polymer beads with the specific functional groups through dissolving and swelling method, which provided the condition for the conjunction of biomolecules and QDs as fluorescent probes. The prepared composites were characterized with UV-Vis, PL, TEM, FTIR, CLSM and conductance titration etc. The results show that QDs are successfully embedded in polymer beads, which breaks the limitation that the conjunction of biomolecules and QDs can be achieved only for those synthesized in aqueous system. __________ Translated from Journal of Shanghai Jiaotong University, 2005, 39(1) (in Chinese)     

Study on the effects of fluorine and oxygen deficiency on YBa2Cu307 byab initio method

The calculations of clusters modeling the fluorine-doping and oxygen deficiency of YBa₂Cu₃0₇ have been performed by the method of all-electronab initio Hartree-Fock with self-consistent crystal field. Results show that in CuO planes electric charge significantly increases, the chemical valence of Cu decreases and the covalent bonding of Cu-O greatly weakens owing to oxygen deficiency, while the effect of F restores the local electronic structure of YBa₂Cu₃O₇. The reported opinion that F occupied the oxygen vacancy in Cu-O chains seems disputable according to the calculated bonding characteristics Project supported by the National Natural Science Foundation of China.     

Generation of Molecular Fields, Quantum Similarity Measures and Related Questions

A straightforward discussion on how to generate molecular fields is developed within the postulates of quantum mechanics. The theoretical formalism points towards the generalization and extension of the well-known molecular field forms, associated to density function and electrostatic molecular potential (EMP), including another category of fields associated to quantum molecular similarity measures. The results show that the new formalism can be easily applied to obtain an unlimited number of new information about molecular behavior.     

Influence of static and dynamical structural changes on ultrafast processes mediated by conical intersections

The technological needs imposed by the exponential miniaturization trend of conventional electronic devices has drawn attention towards the development of smaller and faster devices like ultrafast molecular switches. In recent years molecular switches emerge again in the focus of active and innovative research with state-of-the-art optical tools recording their dynamics in real time. Still many questions about the underlying microscopic mechanism are left open, including potential factors that effect the switching process in either way, improve or worsen it. Due to the complexity of such molecules it is difficult to obtain a global answer from experiment alone. On the other side molecular switches are generally too large for a complete quantum chemical and quantum dynamical calculation. In our group we therefore developed an ab initio based modular model to handle the laser induced quantum dynamics in molecular switches like fulgides. It enables us to study the effect of internal molecular coupling and of the molecular response to external fields. We can investigate the related wave packet dynamics, the switching efficiency and the controllability. Our results focus on the laser induced ring opening in fulgides, which equals one direction of the switching process. Presented are the influence of a conical intersection seam and of time-dependent potentials, mimicking the mean interaction with the environment. Furthermore the relation of controllability and the wave packet's momentum is studied and the influence of potential barriers on the switching dynamics is shown.