Perturbations in the Spectra of the Rydberg Series of a Silver Atom

The main series of a silver atom with n = 5–70 are investigated. Perturbations of the np ² P _1/2,3/2 states with n = 10 and 17 caused by interaction with the selfionization 4d5s5p ⁴ P _1/2,3/2 states are detected. Energies of the selfionization states are determined.     

Quantum Mayer Graphs for Coulomb Systems and the Analog of the Debye Potential

Within the Feynman–Kac path integral representation, the equilibrium quantities of a quantum plasma can be represented by Mayer graphs. The well known Coulomb divergencies that appear in these series are eliminated by partial resummations. In this paper, we propose a resummation scheme based on the introduction of a single effective potential that is the quantum analog of the Debye potential. A low density analysis of shows that it reduces, at short distances, to the bare Coulomb interaction between the charges (which is able to lead to bound states). At scale of the order of the Debye screening length ^–1 _D, approaches the classical Debye potential and, at large distances, it decays as a dipolar potential (this large distance behaviour is due to the quantum nature of the particles). The prototype graphs that result from the resummation obey the same diagrammatical rules as the classical graphs of the Abe–Meeron series. We give several applications that show the usefulness of to account for Coulombic effects at all distances in a coherent way.     

Mechanistic aspects of the dehydration and dehydrohalogenation of halo-hydroxyformaldoxime conformers. A quantum chemical model study

A detailed exploration of the configurational and conformational space of chloro- and bromo-hydroxyformaldoximes, Xhfaox (X = Cl, Br) has been carried out with the aid of the B3LYP level of density functional theory, using the 6-31G(d,p) basis set. The most stable configuration in each series of the Clhfaox and Brhfaox conformers corresponds to the Z-s-cis, s-trans configuration, while the highest energy Z-(s-trans, s-cis) conformers were found at 7.0(7.6) and 6.0(6.6) kcal mol(-1), respectively, at the B3LYP(QCISD(T)) levels of theory. Saddle points were also located on the PES of the Clhfaox and Brhfaox compounds corresponding to Z-(s-cis, s-cis) conformers at 13.8(14.9) and 13.6(14.6) kcal mol(-1), respectively, at the B3LYP(QCISD(T)) levels. Upon dehydration Xhfaox could afford a number of isomeric CXNO species. The dehydration processes of Xhfaox are predicted to be endothermic, the computed heats of reactions found in the range of 20.5 to 86.2 kcal mol(-1) and 15.9 to 100.4 kcal mol(-1) at the B3LYP and QCISD(T) levels, respectively. The reaction pathways for the addition of water to halo-fulminates yielding the most stable Xhfaox conformers was predicted to be concerted with a single transition structure, but are asynchronous with activation barriers of 32.8 and 43.0 kcal mol(-1) for the chloro- and bromo-derivatives, respectively. The PES governing the isomerization reactions of the CXNO isomers have also been calculated, and possible isomerization pathways have been delineated. Upon dehydrohalogenation the Xhfaox conformers yield hydroxy-isocyanate or hydroxy-fulminate, the former being more stable by 31.8(18.8) kcal mol(-1) at the B3LYP(QCISD(T)) levels of theory. The reaction pathways for the addition of HX to hydroxy-isocyanate were predicted to be slightly exothermic, the heats of reactions being -3.2 and -5.5 kcal mol(-1), respectively, and have to surmount high activation barriers of 39.7 and 35.0 kcal mol(-1), respectively. Similarly, the addition of HX to hydroxy-fulminate was predicted to be much more exothermic, the heats of reactions being -34.7 and -37.3 kcal mol(-1), respectively, and have to surmount much lower activation barriers of only 10.5 and 7.5 kcal mol(-1) respectively, at the B3LYP level. Finally, calculated structures, relative stability, and bonding properties of all stationary points located on the PES of the systems and reactions studied are thoroughly discussed with respect to computed electronic properties.     

From "parasitic" association reactions toward the stoichiometry controlled gas phase synthesis of nanoparticles: a theoretically driven challenge for experimentalists

In the present record a model for the gas-phase reactions during the chemical vapor deposition (CVD) processes of group 13-15 materials is presented, based on the results of extensive quantum-chemical modeling. Thermodynamic criteria have been introduced to evaluate the importance of a range of association reactions. For the organometallic and hydride derivatives, association processes are found to be favorable both thermodynamically and kinetically. Formation of high mass association products takes place under CVD conditions, including laser-assisted CVD. Structural and thermodynamic properties of the most important ring and cluster intermediates have been predicted. The stoichiometry-controlled synthesis of the 13-15 ternary alloys and nanoparticles using cluster compounds as single-source precursors is predicted to be viable. The association pathway described may be generalized to the CVD reactions of many binary materials (12-16, 13-16, 13-15, 14-15, 14-16).     

Trace Functionals on Noncommutative Deformations of Moduli Spaces of Flat Connections

We describe an efficient construction of a canonical noncommutative deformation of the algebraic functions on the moduli spaces of flat connections on a Riemann surface. The resulting algebra is a variant of the quantum moduli algebra introduced by Alekseev, Grosse, and Schomerus and Buffenoir and Roche. We construct a natural trace functional on this algebra and show that it is related to the canonical trace in the formal index theory of Fedosov and Nest and Tsygan via Verlinde's formula.     

Traces of Intertwiners for Quantum Groups and Difference Equations

In this Letter we study twisted traces of products of intertwining operators for quantum affine algebras. They are interesting special functions, depending on two weights ,, three scalar parameters q,,k, and spectral parameters z ₁,...,z _N , which may be regarded as q-analogs of conformal blocks of the Wess–Zumino–Witten model on an elliptic curve. It is expected that in the rank 1 case they essentially coincide with the elliptic hypergeometric functions defined by Felder and Varchenko. Our main result is that after a suitable renormalization the traces satisfy four systems of difference equations – the Macdonald–Ruijsenaars equation, the q-Knizhnik–Zamolodchikov–Bernard equation, and their dual versions. We also show that in the case when the twisting automorphism is trivial, the trace functions are symmetric under the permutation , k . Thus, our results generalize those of Etingof and Schiffmann, dealing with the case q=1, and Etingof, Varchenko, and Schiffmann, dealing with the finite-dimensional case.     

Crystal Structure of Level Zero Extremal Weight Modules

We consider the crystal structure of the level zero extremal weight modules V() using the crystal base of the quantum affine algebra constructed in Duke Math. J. 99 (1999), 455–487. This approach yields an explicit form for extremal weight vectors in the U ^– part of each connected component of the crystal, which are given as Schur functions in the imaginary root vectors. We show the map induces a correspondence between the global crystal base of V() and elements .     

Equivalence Postulate and Quantum Origin of Gravitation

We suggest that quantum mechanics and gravity are intimately related. In particular, we investigate the quantum Hamilton–Jacobi equation in the case of two free particles and show that the quantum potential, which is attractive, may generate the gravitational potential. The investigation, related to the formulation of quantum mechanics based on the equivalence postulate, is based on the analysis of the reduced action. A consequence of this approach is that the quantum potential is always non-trivial even in the case of the free particle. It plays the role of intrinsic energy and may in fact be at the origin of fundamental interactions. We pursue this idea, by making a preliminary investigation of whether there exists a set of solutions for which the quantum potential can be expressed with a gravitational potential leading term which alone would remain in the limit 0. A number of questions are raised for further investigation.     

第Ⅱ种强度不等的非对称两态叠加多模叠加态光场的偶数阶等阶N次方Y压缩

本文构造了由多模复共轭相干态的相反态|{-Z_j^(a)*}>_q与多模虚共轭相干态的相反态|{-iZ_j^(b)*}>_q这两者的线性叠加所组成的第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)>_q,利用多模压缩态理论研究了态|Ψ_Ⅱ^(ab)>_q的任意偶数阶等阶N次方Y压缩特性.结果发现:1)在压缩阶数N取偶数,即N=2p的条件下,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要构成态|Ψ_Ⅱ^(ab)>_q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位都不相等,亦即R_j^(a)≠R_j^(b)和φ_j^(a)≠φ_j^(b)(j=1,2,3,…,q),并且 ,则当满足一定的量子化条件(或者在一些闭区间内连续取值)时,态|Ψ_Ⅱ^(ab)>_q总可呈现出周期性变化的、任意偶数阶的等阶N次方Y压缩效应.2)在N=2p且p=2m+1(m=0,1,2,3,…,…)的条件下,若R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),态|Ψ_Ⅱ^(ab)>_q则可呈现出等阶N次方Y压缩简并现象.     

第Ⅰ种非对称两态叠加多模叠加态光场的偶数阶等阶N次方Y压缩

本文利用多模压缩态理论,研究了第Ⅰ种非对称两态叠加多模叠加态光场|Ψ_Ⅰ^(ab)Ⅰ>_q的偶数阶等阶N次方Y压缩特性.结果发现:在压缩阶数N取偶数情况下,只要构成态|Ψ_Ⅰ^(ab)Ⅰ>_q的两个量子光场态的强度(即平均光子数)不相等,则当各模的初始相位φ_j^(a)、φ_j^(b)(j＝1,2,3,…,q)、态间的初始相位差(θ_pq^(bI)-θ_nq^(aR))以及与上述的两个量子光场态相对应的各单模相干态光场的光子干涉项之和 ＝[R_j^(a)R_j^(b)cos(φ_j^(a)-φ_j^(b))]等满足一定条件时,态|Ψ_Ⅰ^(ab)Ⅰ>_q可呈现出周期性变化的、任意偶数阶的等阶N次方Y压缩效应.这一结果与现有文献报道的结果截然不同.