On Frobenius algebras and the quantum Yang-Baxter equation

It is shown that every Frobenius algebra over a commutative ring determines a class of solutions of the quantum Yang-Baxter equation, which forms a subbimodule of its tensor square. Moreover, this subbimodule is free of rank one as a left (right) submodule. An explicit form of a generator is given in terms of the Frobenius homomorphism. It turns out that the generator is invertible in the tensor square if and only if the algebra is Azumaya.

     

Femtosecond dynamics of secondary radiation formation from quantum well excitons

The time-resolved secondary emission of resonantly created excitons in GaAs quantum wells is studied using femtosecond up-conversion spectroscopy. The behaviour of the rise and decay of the secondary emission and reflectivity in quantum wells is strongly dependent upon the disorder at the interfaces, the exciton density and the temperature. In the case of low densities and temperatures the emission is independent of the exciton density and rises quadratically in time, in excellent agreement with recent theory for Rayleigh scattering from two-dimensional excitons subjected to disorder. These rise times are compared directly with times measured by time-integrated four-wave mixing (FWM). The comparison of the dynamics displayed in time-resolved secondary radiation and time-integrated FWM provide a clear understanding of the coherence properties of QW excitons in the first few picoseconds after excitation. High-contrast oscillations that are due to quantum beats between the heavy- and light-hole 1s-states are seen. The visibility decay at very low densities is long ps and is related to the action of potential fluctuations on the scattering of heavy-hole and light-hole excitons.     

Zeroth and second laws of thermodynamics simultaneously questioned in the quantum microworld

A new and rather trivial model is suggested with mechanism that implies simultaneous violation of the zeroth and the second laws of thermodynamics. Mathematically rigorous quantum theory reduces to a trivial application of the Golden rule formula. It yields exciton on-energy-shell diffusion caused by bath-nonassisted excitation hopping between tails of different exciton site levels ε₁ < ε₂ broadened by bath-assisted finite life-time effects. The elastic character of the hopping implies 1 ↔ 2-symmetric transfer rate W. Thus the net diffusion exciton flow W(P ₁ - P ₂) and also, as argued, the net energy flow are possible due to different near-to-equilibrium exciton populations P ₁ > P ₂. As the sites are provided with two different baths, the population imbalance and the flows survive even for slightly different local bath temperatures T ₁ < T ₂ < T ₁ε₂/ε₁. Thus spontaneous exciton and also energy flows against temperature step become possible, in contradiction with the Clausius form of the second law. Violations of both the laws disappear in the high-temperature, i.e. classical limit Received 16 May 2001 and Received in final form 20 September 2001     

类氢及碱金属原子激发态寿命的半经典计算公式

根据对应原理,得到了类氢原子能态平均寿命半经典的计算公式τ(n,l),然后利用相对论单通道量子数亏损理论进行推广,得到用来计算考虑总角动量J的激发态寿命公式τ(n,l,l+1/2)和τ(n,l,l-1/2),利用单通道量子数亏损理论得到了碱金属原子n、l远大于1时激发态寿命的半经典公式τ(n.l)=τ0(m+M/nm/v/+M)2v7l(l+1/2)/n4,其计算结果和实验数据符合的很好.     

Energy levels in doped SiGe quantum well studied by admittance spectroscopy

SiGe/Si quantum wells (QWs) with different Boron doping concentrations were grown by molecular beam epitaxy (MBE) on p-type Si(1 0 0) substrate. The activation energies of the heavily holes in ground states of QWs, which correspond to the energy differences between the heavy hole ground states and Si valence band, were measured by admittance spectroscopy. It is found that the activation energy in a heavily doped QW increases with doping concentration, which can be understood by the band alignment changes due to the doping in the QWs. Also, it is found that the activation energy in a QW with a doping concentration of 2 × 10²⁰ cm⁻³ becomes larger after annealing at a temperature of 685 °C, which is attributed to more Boron atoms activation in the QW by annealing.     

40,48Ca+90,96Zr融合反应的动力学模型研究

应用改进的量子分子动力学模型,在严格挑选初始核考虑弹靶结构效应的基础上,研究了近垒和垒上融合反应^40,48Ca+^90,96Zr. 研究表明: 4个反应的理论计算截面与实验值很好符合; 丰中子反应⁴⁰Ca+⁹⁶Zr的垒下融合截面比其他3个反应有明显增强的现象.为了理解丰中子反应⁴⁰Ca+⁹⁶Zr与⁴⁰Ca+⁹⁰Zr相比垒下融合截面增强,而Ca+⁹⁶Zr垒下融合截面没有明显增强的原因, 进一步分析了484个反应的融合位垒,中子转移与融合位垒的关系、中子转移与Q值的关系,结果表明: 正反应Q值会引起核子(特别是中子)转移的增强,从而导致动力学融合位垒的下降和垒下融合截面增强.     

双参数变形玻色湮没算符高次幂的本征态及其量子统计性质

本文构造了双参数变形玻色湮没算符高次幂a^'k(k≥3)的k个正交归一木征态的数学结构,发现它们能构成一个完备的Hilbert空间,并且讨论了它们的量子统计性质.     

Environment-induced decoherence II. Effect of decoherence on Bell''s inequality for an EPR pair

According to Bell's theorem, the degree of correlation between spatially separated measurements on a quantum system is limited by certain inequalities if one assumes the condition of locality. Quantum mechanics predicts that this limit can be exceeded, making it nonlocal. We analyse the effect of an environment modelled by a fluctuating magnetic field on the quantum correlations in an EPR singlet as seen in the Bell inequality. We show that in an EPR setup, the system goes from the usual ‘violation’ of Bell's inequality to a ‘non-violation’ for times larger than a characteristic time scale which is related to the parameters of the fluctuating field. We also look at these inequalities as a function of the spatial separation between the EPR pair.     

A theoretical approach to substituent effects: Interaction between directly bonded groups in the isoelectronic series XNH3+, XCH3, and XBH3−

Ab initio molecular orbital theory including full geometry optimization at the 4-31G level is used to examine the interactions between substitutents X(X = Li, BeH, BH₂, CH₃, NH₂, OH and F) and substrates Y(Y = NH₃⁺, CH₃, BH₃^?) in the isoelectronic series XNH₃⁺, XCH₃ and XBH₃^?. The results indicate that the interaction energies are dominated by σ-effects. NH₃⁺ is found to interact favorably with the σ-donors (e.g. Li, BeH and BH₂) and unfavorably with the σ-acceptors (e.g. F, OH, NH₂). The reverse pattern a observed for XBH₃^?. The range of interaction energies for XCH₃ is considerably smaller than for XNH₃⁺ and XBH₃^?.     

Geometry,stability and aromaticity of β-diketiminate-coordinated alkaline-earth compounds

Alkaline-earth (Ae) metals have attracted a wealth of interdependent research from synthetic chemists. In Ae-catalyzed organometallic reactions, β-diketiminate is a typical ligand used to stabilize Ae catalysts by forming six-membered rings comprising Ae metals. Herein, studies focusing on the configuration of β-diketiminate-coordinated Ae compounds observed that the CC and CN bonds are homogeneous and unchanged. Furthermore, energetic studies observed that the formation of the Ae-incorporated six-membered rings results in enhanced stability of >20 kcal/mol. The nucleus-independent chemical shifts, anisotropy of the induced current density, and molecular orbital analyses demonstrated the non-aromaticity of the β-diketiminate-coordinated Ae compounds. The improved stability of these compounds can be explained by the delocalization of the π electrons derived from the β-diketiminate moiety.