Systematic Study on Triaxial Superdeformed Bands of Hf Isotopes

Properties of the triaxiai superdeformed （TSD） bands of Hf isotopes are investigated systematicaily within the supersymmetry scheme including many-body interactions and a perturbation possessing the SO（5） （or SU（5）） symmetry on the rotational symmetry. Quantitatively good results of the γ-ray energies, the dynamical moments of inertia, and the spin of the TSD bands in Hf isotopes are obtained. It shows that this approach is quite powerful in describing the properties of the triaxial superdeformation in Hf isotopes.     

Description of Rotation Bands in 157,158Er at Ultrahigh Spin

Properties of the four rotation bands, ¹⁵⁷Er(1,2) and ¹⁵⁸Er(1,2), at ultrahigh spin are investigated within the supersymmetry scheme including many-body interactions and possessing the SO(5) (or SU(5)) symmetry on the rotational symmetry. Quantitatively good results of the  γ-ray energies and the dynamical moments of inertia in the rotation bands in ¹⁵⁷Er and ¹⁵⁸Er at ultrahigh spin are obtained. We theoretically predict that the competition between the anti-pairing and pairing effects may exist in ¹⁵⁷Er(1,2) and ¹⁵⁸Er(2) bands states. In ¹⁵⁸Er(1) band state, the favoure-pairing effects may exist and the SO(5) (or SU(5)) symmetry play a dominant role. There may be sphere coexisting with headecupole deformed in ¹⁵⁸Er(1) rotation band state.     

Robust H∞ observer-based of a class of complex control for synchronization dynamical networks

This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities （LMIs）. The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Novel exact solutions of coupled nonlinear Schrōdinger equations with time-space modulation

We construct various novel exact solutions of two coupled dynamical nonlinear Schrōdinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrōdinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrrdinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.     

Global dynamical analysis of vibrational manifolds of HOCl and HOBr under anharmonicity and Fermi resonance:the dynamical potential approach

The vibrational dynamics of HOCl and HOBr between bending and OCl/OBr stretching coordinates with anharmonicity and Fermi coupling is studied with the classical dynamical potential approach. The quantal vibrational dynamics is mostly mapped out by the classical nonlinear variables such as fixed points, except for the state energies, which are quantized. This approach is global in the sense that the focus is on a set of levels instead of individual ones. The dynamics of HOBr is demonstrated to be less complicated. The localized modes along the OCl/OBr stretching coordinates are also shown to have O-Br bonds more prone to dissociation.     

Analysis of dynamical properties for the two-site Bose Hubbard model with an algebraic method

In this work, we propose an algebraic recursion method to study the dynamical evolution of the two-site Bose- Hubbard model. We analyze its properties from the viewpoints of single partite purity, energy, and trace distance, in which the model is considered as a typical bipartite system. The analytical expressions for the quantities are derived. We show that the purity can well reflect the transition between different regimes for the system. In addition, we demonstrate that the transition from the delocalization regime to the self-trapping regime with the ratio r/increasing not only happens for an initially local state but also for any initial states. Furthermore, we confirm that the dynamics of the system presents a periodicity for η = 0 and the period is tc =π/2J when the initial state is symmetric.     

Entropy of Quantum Dynamical Systems and Sufficient Families in Orthomodular Lattices with Bayessian State

The purpose of the present paper is to study the entropy hs（Ф） of a quantum dynamical systems Ф = （ L, s, Ф）, where s is a bayessian state on an orthomodular lattice L. Having introduced the notion of entropy hs（ Ф, A） of partition A of a Boolean algebra B with respect to a state s and a state preserving homomorphism Ф, we prove a few results on that, define the entropy of a dynamical system hs（Ф）, and show its invariance. The concept of sufficient families is also given and we establish that hs （Ф） comes out to be equal to the supremum of hs （Ф,A）, where A varies over any sufficient family. The present theory has then been extended to the quantum dynamical system （ L, s, Ф）, which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system （B, s0, Ф）, where B is a Boolean algebra and so is a state on B.     

Exploring the light-quark interaction

Two basic motivations for an upgraded JLab facility are the needs： to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking （DCSB）; and to understand nucleon structure and spectroscopy in terms of QCD＇s elementary degrees of freedom. During the next ten years a programme of experiment and theory will be conducted that can address these questions. We present a Dyson- Schwinger equation perspective on this effort with numerous illustrations, amongst them： an interpretation of string~breaking; a symmetry-preserving truncation for mesons; the nucleon＇s strangeness σ-term; and the neutron＇s charge distribution.     

Cooling Torsional Nanomechanical Vibration by Spin-Orbit Interactions

We propose and study a spin-orbit interaction based mechanism to actively cool down the torsional vibration of a nanomechanical resonator made by semiconductor materials. We show that the spin-orbit interactions of electrons can induce a coherent coupling between the electron spins and the torsional modes of nanomechanical vibration. This coupling leads to an active cooling for the torsional modes through the dynamical thermalization of the resonator by the spin ensemble.     

Entanglement dynamics of a moving multi-photon Jaynes-Cummings model in mixed states

Using the algebraic dynamical method,the entanglement dynamics of an atom-field bipartite system in a mixed state is investigated.The atomic center-of-mass motion and the field-mode structure are also included in this system.We find that the values of the detuning and the average photon number are larger,the amplitude of the entanglement is smaller,but its period does not increase accordingly.Moreover,with the increase of the field-mode structure parameter and the transition photon number,the amplitude of the entanglement varies slightly while the oscillation becomes more and more fast.Interestingly,a damping evolution of the entanglement appears when both the detuning and the atomic motion are considered simultaneously.     

Exponential Synchronization of Uncertain Complex Dynamical Networks with Delay Coupling

This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.     

Dynamical Symmetry Breaking of Maximally Generalized Yang-Mills Model and Its Restoration at Finite Temperatures

In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Vang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.     

Dynamical Suppression of Nonlocal Decoherence in Two-State Quantum Systems

Nonlocal decoherence of two qubits due to Pure phase damping has been investigated. We have proposed a scheme to keep the entanglement of two qubits from nonlocal decoherence. By applying a series of ±π pulses, nonlocal decoherence can be thoroughly suppressed.     

Quantum phase transitions of fermionic atoms in an anisotropic triangular optical lattice

The effect of anisotropy caused by a confining potential on the properties of fermionic cold atoms in a triangular optical lattice is systematically investigated by using the dynamical cluster approximation combined with the continuous time quantum Monte–Carlo algorithm.The quantum phase diagrams which reflect the temperature–interaction relation and the competition between the anisotropic parameter and the interaction are presented with full consideration of the anisotropy of the system.Our results show that the system undergoes a transition from Fermi liquid to Mott insulator when the repulsive interaction reaches a critical value.The Kondo effect also can be observed in this system and the pseudogap is suppressed at low temperatures due to the Kondo effect.A feasible experiment protocol to observe these phenomena in an anisotropic triangular optical lattice with cold atoms is proposed,in which the hopping terms are closely related to the lattice confining potential and the atomic interaction can be adjusted via the Feshbach resonance.     

Estimating Topology of Discrete Dynamical Networks

In this paper, by applying Lasalle＇s invariance principle and some results about the trace of a matrix, we propose a method for estimating the topological structure of a discrete dynamical network based on the dynamical evolution of the network. The network concerned can be directed or undirected, weighted or unweighted, and the local dynamics of each node can be nonidentical. The connections among the nodes can be all unknown or partially known, Finally, two examples, including a Henon map and a central network, are illustrated to verify the theoretical results.     

Invariant Sets and Exact Solutions to Nonlinear Diffusion Equations with x-Dependent Convection and Absorption

In this paper, we introduce a new invariant set Eo={u：ux=f＇（x）F（u）＋ε[g＇（x）-f＇（x）g（x）]F（u）×exp（-∫^u1/F（z）dz）}where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to be determined. The invariant sets and exact sohltions to nonlinear diffusion equation ut = （ D（u）ux）x ＋ Q（x, u）ux ＋ P（x, u）, are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set Eo.     

Spectroscopic investigations on NO＋（X1∑＋, a3∑＋, A1II） ion using multi-reference configuration interaction method and correlation-consistent sextuple basis set augmented with diffuse functions

Three low-lying electronic states （X1∑, a3∑＋, and A1II） of NO＋ ion are studied using the complete active space self-consistent-field （CASSCF） method followed by highly accurate valence internally contracted multi-reference configuration interaction （MRCI） approach in combination of the correlation-consistent sextuple basis set augmented with diffuse functions, aug-cc-pV6Z. The potential energy curves （PECs） of the NO＋（X1∑＋, a3∑＋, A1II） are calculated. Based on the PECs, the spectroscopic parameters Re, De, We, WeXe, ae, Be, and D0 are reproduced, which are in excellent agreement with the available measurements. By numerically solving the radial SchrSdinger equation of nuclear motion using the Numerov method, the first 20 vibrational levels, inertial rotation and centrifugal distortion constants of NO＋（X1∑＋, a3∑＋, A1II） ion are derived when the rotational quantum number J is equal to zero （J = 0） for the first time, which accord well with the available measurements. Finally, the analytical potential energy functions of these states are fitted, which are used to accurately derive the first 20 classical turning points when J = 0. These results are compared in detail with those of previous investigations reported in the literature.     

Differential Representations of SO（4） Dynamical Group

In this paper we present systematic differential representations for the dynamical group SO（4）. These representations include the left and the right differential representations and the left and the right adjoint differential representations in both the group parameter space and its coset spaces. They are the generalization of the differential representations of the SO（3） rotation group in the Euler angles. These representations may find their applications in the study of the physical systems with SO（4） dynamical symmetry.     

Gaussian Integral Formula for Quaternions Based on Class Operator＇s Formula of Rotation Group

Abstract There exists rare integration formulas over quaternions due to the noncommutativity of quarternions multplication. Based on the class operator＇s formula of rotation group we derive a Gaussian integral formula for quaternions, which is similar in form to the integration for coherent state＇s completeness relation.     

QCD Approach to B →Dπ Decays and CP Violation

The branching ratios and CP violations of the B →Dπ decays, including both the color-allowed and the color-suppressed modes, are investigated in detail within QCD framework by considering all diagrams that lead to three effective currents of two quarks. An intrinsic mass scale as a dynamical gluon mass is introduced to treat the infrared divergence caused by the soft collinear approximation in the endpoint regions, and the Cutkosky rule is adopted to deal with a physical-region singularity of the on mass-shell quark propagators. When the dynamical gluon mass μg is regarded as a universal sca/e, it is extracted to be around μg = 440 MeV from one of the well-measured B →Dπ decay modes. The resulting predictions for all branching ratios are in agreement with the current experimental measurements. As these decays have no penguin contributions, there are no direct CP asymmetries. Due to interference between the Cabibbo-suppressed and the Cabibbo-favored amplitudes, mixing-induced CP violations are predicted in the B →D^±π^±↓ decays to be consistent with the experimental data at 1-σ level. More precise measurements will be helpful to extracting weak angle 2β＋γ.