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Effect of an impurity on 3-electron quantum dots in magnetic fields

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Science china({1.,Mechanics & Astronomy) 2004年第5期47卷 521-530页

作者： LIU Yimin1.2. HUANG Gangming1.& BAO Chengguang1.1. {1. of physics, Zhongshan {2., Guangzhou 51.2.5, china 2. {1. of physics, Shaoguan {2., Shaoguan 51.0}05, china department of {1. Zhongshan University Guangzhou China department of {1. Shaoguan University Shaoguan China

The ground-state property of a 2.dimensional 3-electron quantum dot (QD) subjected to an external magnetic fieldB and affected by an impurity is studied. The impurity is located at thez-axis by a distanced from the plane of the dot. The evolution of the angular momentumL o and the spinS o of the ground state in accordance withB andd has been calculated, and the results are summarized and plotted in a (L o,S o) diagram. The spatial distribution of the electrons (the size and the geometric features) and the optical absorption have also been investigated. The (L o S o) diagram indicates thatL o andS o may jump whend and/orB vary. It was found that, due to the constraints arising from symmetry, each symmetric geometry is accessible only to a specific group of states having specificL o andS o.

关键词： quantum dot, ground state, charged impurity, magnetic field.

The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice

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Science china({1.,Mechanics & Astronomy) 2005年第2期48卷 150-157页

作者： XU Quan1.& TIAN Qiang2.1. Scientific and Technological Office, Daqing Teacher College, Daqing 1.371.0} china 2. department of {2. , Beijing normal university, Beijing 1.0875, china Scientific and Technological Office Daqing Teacher College Daqing China department of {1. Beijing Normal University Beijing China

The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2.) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.

关键词： two-dimensional nonlinear lattice, quasi-one-dimensional nonlinear lattice, kink-soliton, antikink-soliton.

Density-functional formula for strongly correlated systems

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Progress in Natural Science:Materials International 2005年第5期15卷 395-401页

作者： WANG Huaiyu1.*, HAN Rushan2.and CHEN Nanxian1.1. {1. of physics, Tsinghua {2., Beijing 1.0084, china 2. {1. of physics, Peking {2., Beijing 1.0871. china) Dept. of Phys. Tsinghua Univ. Beijing 100084 China Dept. of Phys. Peking Univ. Beijing 100871 China

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.

关键词： density-functional theory strongly correlated systems doubly-occupied orbital two-particle wave function self-consistent equations.

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1.& GUO Boling2.1. {1. of Mathematics, Beijing normal {2., Beijing 1.0875, china 2. Institute of Applied physics and Computational Mathematics, Beijing 1.0080, china department of Mathematics Beijing Normal University Beijing China Institute of Applied physics and Computational Mathematics Beijing China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

Stochastic resonance in surface catalytic oxidation of carbon monoxide induced by colored noise

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Science china Chemistry 2004年第2期47卷 106-112页

作者： GONG Yubing1.2. HOU Zhonghuai1.& XIN Houwen1.1. {1. of Chemical physics, {2. of Science and Technology of china, Hefei 2.002., china 2. {1. of physics, Yantai Teachers {2., Yantai 2.402., china department of Chemical {1. University of Science and Technology of China Hefei China department of {1. Yantai Teachers University Yantai China

The dynamical behavior of surface catalytic oxidation reaction of Pt(1.0)/CO+O2.modulated by colored noise, under the condition of specific temperature, has been investigated when the partial pressure of CO gas is near the supercritical Hopf bifurcation point. By computer simulation the oscillation and stochastic resonance induced by colored noise are observed. The influences of the intensity and correlation time of colored noise on stochastic resonance are discussed. The range of sensitivity of the system to the environmental fluctuation is analyzed.

关键词： colored noise, stochastic resonance, surface catalytic reaction of Pt(1.0)/CO+O2. supercritical Hopf bifurcation, signal-to-noise ratio (SNR).

Internal noise stochastic resonance in CO oxidation on nm-sized palladium particles

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Science china Chemistry 2005年第5期48卷 395-401页

Based on a stochastic mesoscopic model, the influence of internal noise on the oscillatory kinetics of the catalytic oxidation of CO on nm-sized palladium particles is studied, using the chemical Langevin equations, Poisson approximation algorithm, and exact stochastic simulation algorithm. The reaction rate oscillations are of stochastic nature due to considerable internal noise in such mesoscopic systems. It is found that the performance of the stochastic oscillations undergoes a maximum with the variation of internal noise level for a given CO partial pressure, which demonstrates the occurrence of internal noise stochastic resonance. This phe-nomenon implies that optimal internal noise would favor the reaction rate oscillation of CO oxi-dation on nm particles. Such a phenomenon is robust to the change of external parameters, such as CO pressures.

关键词： nanometer-sized palladium particles, surface catalytic CO oxidation, internal noise, stochastic resonance, chemical Langevin equation.

Theoretical study on thermal decomposition of azoisobutyronitrile in ground state

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Science china Chemistry 2004年第5期47卷 373-380页

作者： SUN Chengke1.2. ZHAO Hongmei1.& LI Zonghe1.1. {1. of Chemistry, Beijing normal {2., Beijing 1.0875, china 2. {1. of Chemistry, Qujing normal College, Qujing 655000, china Dept. of Chem. Beijing Normal Univ. Beijing 100875 China Dept. of Chem. Qujing Normal Coll. Qujing 655000 China

The thermal decomposition mechanisms of azoisobutyronitrile (AIBN) in the ground state have been investigated systematically. Based on the potential energy surfaces (PES) of various possible dissociation paths obtained using the semiempirical AM1.method with partial optimization, the density function theory B3LYP/6-31.G* method was employed to optimize the geometric parameters of the reactants, the intermediates, the products and the transition states, which were further confirmed by the vibrational analysis. The obtained results show that the re- action process of the two-bond (three-body) simultaneous cleavage Me2.CN)C─ N=N─ C(CN)Me2. 2.e2.CN)C?+N2.is much more favorable than the reaction process of the two one- bond asynchronous cleavage Me2.CN)CN=N─C(CN)Me2.? Me2.CN)CN=N?+ Me2.CN)C?? Me2.CN)C?+ N2. It was suggested that the electron shrinking effect of double bond (─N=N─) in AIBN and the stabilities of the Me2.CN)C?radical as well as N2.molecule are main factors of leading to the reaction proceeding in the former pathway. The calculation results were consistent with all the experimental facts.

关键词： azoisobutyronitrile, radicals, thermal decomposition, density function theory (DFT).

Superconductivity of small metal grains

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Science china({1.,Mechanics & Astronomy) 2005年第4期48卷 431-441页

作者： ZHENG Renrong1.CHEN Zhiqian2.& ZHU Shunquan1.3 1. {1. of physics, Shanghai {2. university, Shanghai 2.02.4, china 2. {1. of physics, Southwest {2. university, Chongqing 40071., china 3. {1. of Computer and Electric Technology, Shanghai Business School, Shanghai 2.1.00, china department of {1. Shanghai Normal University Shanghai China department of {1. Southwest Normal University Chongqing China department of Computer and Electric Technology Shanghai Business School Shanghai China

The formulas of the energy gap and superconducting critical temperature appropriate for systems with both odd and even number of electrons are derived; the bases of the derivations are BCS theory and energy level statistics. Numerical results qualitatively agree with the experimental phenomena. i.e., the superconductivity of small metallic grains will first enhance then decrease to zero when the grain are getting smaller and smaller. The calculations indicate that the above phenomena happen in the metallic grains belonging to Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary ensemble (GUE) with zero spin; The superconductivity of small metallic grains in Gaussian Symplectic Ensemble (GSE) will monotonically decrease to zero with the decreasing of the grain size. The analyses suggest that the superconductivity enhancements come from pairing and the balance of the strengths between spin-orbital coupling and external magnetic field. In order to take the latter into account, it is necessary to include the level statistics given by Random Matrix Theory (RMT) in describing small metallic grains.

关键词： size effect, superconductivity enhancements, small metallic grains.

Density functional study on enantioselective reduction of keto oxime ether with borane catalyzed by oxazaborolidine

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Science china Chemistry 2006年第4期49卷 296-307页

作者： LI Ming1. ZHENG Wenxu2.& TIAN Anmin2.1. department of Chemistry, Southwest-china {2. university, Chongqing 40071., china 2. department of Chemistry, Sichuan university, Chengdu 61.064, china department of Chemistry Southwest-China Normal University Chongqing China department of Chemistry Sichuan University Chengdu China

The enantioselective reduction of keto oxime ether with borane catalyzed by oxazaborolidine is discussed by the density functional theory (DFT) method. The main intermediates and transition states for this reaction are optimized completely at the B3LYP/6-31.(d) level, and the transition states are verified by vibrational modes. As shown, the chirality-controlled steps for this re- action are the hydride transfer from borane to carbonyl carbon and oxime carbon of keto oxime ether, and the chirality for the reduced products is determined in these two reaction steps. In all examined reaction paths, the first hydride is transferred via a six-membered ring and the second hydride via a five-membered ring or a four-membered ring.

关键词： keto oxime ether, oxazaborolidine, enantioselective reduction, DFT.