Finite Hopf Algebras and Bidifferential Structures

In this Letter we show the existence of bidifferential structures on finite Hopf algebras, which arise from quantum groups at roots of unity.     

Properties of Unsymmetrical Parabolic Confinement Potential Quantum Dot Qubit

On the condition of electric-LO phonon strong coupling in unsymmetrical parabolic confinement potential quantum dot （QD）, we obtain the eigenenergies of the ground state and the first-excited state, the eigenfunctions of the ground state, and the first-excited state by using variational method of Pekar type. This system in QD may be employed as a two-level quantum system-qubit. When the electron is in the superposition state of the ground state and the first-excited state, we obtain the time evolution of the electron density. The relations both the probability density of electron and the period of oscillation with the electron-LO-phonon coupling strength, the confinement strengths in the xy-plane and the z-direction are discussed.     

k紧优双环网的无限族的构造

双环网是计算机互连网络和通讯系统的一类重要拓扑结构,已广泛应用于计算机互连网络拓扑结构的设计中.利用L形瓦理论,结合中国剩余定理和二次同余方程的性质,给出了不同于参考文献中的任意k紧优双环网的无限族的构造方法,证明了对任意正整数k,若n(t)=3t2 At B,A=1,3,5,对于一定的B＞(k 1)2,均存在正整数t,使得{G(n(t);s(t))}是k紧优双环网的无限族,而且这样的无限族有无穷多类.作为定理的应用,给出了多类新的k紧优双环网的无限族.     

Further Study of A-Related Quantum Interference of П-State Diatomic on Collision-Induced Rotational Energy Transfer

In our previous theoretical studies [Meng-Tao Sun, Yong-Qing Lee, and Feng-Cai Ma, Chem. Phys.Lett. 371 (2003) 342], we have reported the quantum interference on collision-induced rotational energy transfer on CO (A1П, v = 3) with inert gases, which originates from the difference between the two A-related collision potential energy surfaces. The interference angle, which measures the degree of coherence, is presented in this paper. Based on the time-dependent first order Born approximation, taking into account the anisotropic Lennard-Jones interaction potentials, the relation of the interference angle with the factors, including experimental temperature, partner, and rotational quantum number, are obtained. The changing tendencies with them are discussed. This theoretical model is important to understanding and performing this kind of experiment.     

Double Hopf bifurcation for van der Pol-Duffing oscillator with parametric delay feedback control

The stability and bifurcation of a van der Pol-Duffing oscillator with the delay feedback are investigated, in which the strength of feedback control is a nonlinear function of delay. A geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and Hopf bifurcations. The Hopf bifurcation curves and multi-stable regions are obtained as two parameters vary. Some weak resonant and non-resonant double Hopf bifurcation phenomena are observed due to the vanishing of the real parts of two pairs of characteristic roots on the margins of the “death island” regions simultaneously. By applying the center manifold theory, the normal forms near the double Hopf bifurcation points, as well as classifications of local dynamics are analyzed. Furthermore, some quasi-periodic and chaotic motions are verified in both theoretical and numerical ways.     

Quantum non-Markovian Langevin equations and transport coefficients for an inverted oscillator

Based on the non-Markovian quantum Langevin equations, we obtain time-dependent transport coefficients for an inverted oscillator coupled linearly in the coordinate to a thermostat. We comparatively analyze the diffusion coefficients for harmonic and inverted oscillators and study the role of quantum statistical effects in the passage through a parabolic barrier. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 425–443, September, 2008.     

The deconfining phase transition in lattice quantum chromodynamics

We present a large-scale Monte Carlo calculation of the deconfining phase transition temperature in lattice quantum chromodynamics without fermions. Using the Wilson action, the transition temperature as a function of the lattice couplingg is consistent with scaling behavior dictated by the perturbativeα function for 6/g²>6.15. Speaker at the conference; on leave from CRIP, Budapest.     

Density functional theory for a model of nonuniform liquid metal in partially ionized states

Summary The problem of the electronic, ionic and atomic density profiles in a nonuniform liquid metal which can locally exist in partially ionized states is examined using the density functional formalism. Ions and electrons are allowed to bind into atoms through a ?reaction? governed by the mass action law. Formally exact equations for the density profiles are given in terms of the inverse response matrix of the nonuniform system, which consists of two terms: the first corresponding to to a mixture of ions, electrons and structureless atoms and the other to the atomic internal degrees of freedom. Approximate schemes are proposed for both contributions, stressing, in partieular, i) how ionization of the atoms arises with increasing density and the relation with Mott’s criterion for the metal-insulator transition, and ii) the usefulness of a weak-coupling assumption for interspecies correlations. This formalism used together with properly parametrized trial functions for the density profiles should be particularly useful for studying the liquid-vapour interface of alkali metals.

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Riassunto Il lavoro usa il formalismo del funzionale di densità per discutere la determinazione dei profili di densità in un fluido non omogeneo che può trovarsi localmente in stati di ionizzazione parziale. Con riferimento specifico ai metalli alcalini, la formazione di atomi per legame di ioni ed electtroni è descritta come una ?reazione? governata dalla legge di azione di massa. Le condizioni di equilibrio microscopico del fluido sono espresse tramite una matrice di risposta in cui appaiono due contributi, associati rispettivamente ai gradi di libertà interni degli atomi e ad una miscela di tre specie di particelle senza struttura interna. Si propongono quindi schemi approssimati per il calcolo di questi due contributi, con attenzione particolare all’uso di teorie perturbative e alla relazione tra grado di ionizzazione locale e densità localle, in connessione col criterio di Mott per la transizione isolante-metallo. Il formalismo proposto è in particolare appropriato per lo studio dell’interfaccia liquido-vapore in metalli alcalini.

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Резюме Используя функционала плотности, исследуется проблема профилей электронной, ионной и атомой ллотностей В неоднодном зидком металле, которий мозет локалщно существоватщ в частично иониэированных состояних. Ионы и электроны могут şвяэыватщся в атомщ череэ ?реакцию, определяемую эаконом дейşтвуюших масс. Приводятся формалщно точные уравнения для профнлеи плотности в термина⇆ обратной матрици отклика для неоднородной системы, которая состоит иэ двух чуленов: первий соответствует ссмеси ионов, электронов и бесстрктурных атмов и второй член соответствует атомным внутренним степеням свобды. Предлагаются приближенные схемы для обоых вкладов, обрашая особое бнмание, в частности, 1) как иониэация атомов воэликает бри увеличени влотности, на свяэы с критерием Мота для берехода ?металл-иеолятор?, и 2) на полеэносты предположения слабой свяэи для межвидовых кореляций. Предложенный Формалиэм, исполыеовалный вместе с параметриэованными пробными функциями для профилей плотнорти, окаэываетця оробенне полеэным для исследования грраницы ?жидкостъ-пар? в шелочлых металлах.