Table of contents

This paper briefly introduces the five types of the surgical operations in knot theory and obtains the expression of single qubit quantum logic gate in terms of these surgical operations.

Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.

Based on the symbolic computational system — Maple, the similarity reductions of a Lax pair for the (2+1)-dimensional differential Sawada–Kotera (SK) equation by the classical Lie point group method, are presented. We obtain several interesting reductions. Comparing the reduced Lax pair's compatibility with the reduced SK equation under the same symmetry group, we find that the reduced Lax pairs do not always lead to the reduced SK equation. In general, the reduced equations are the subsets of the compatibility conditions of the reduced Lax pair.

Using the modified CK's direct method, we derive a symmetry group theorem of (2+1)-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of (2+1)-dimensional dispersive long-wave equations are obtained.

Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto–Sivashinsky (KS) equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here.

With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.

Since product metric on AdS space has played a very important role in Lorentz version of AdS/CFT correspondence, the Yang–Mills equation on AdS space with this metric is considered and a static solution is obtained in this paper, which helps to understand the AdS/CFT correspondence of Yang–Mills fields.

We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties for the system with PDM are also discussed. We give the corresponding effective potentials for several mass functions, the systems with such potentials are isospectral to the usual harmonic oscillator.

Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov–Bohm effect (AB) and external scalar potential. For the spin particles the problem with the magnetic field is that it introduces a singularity into wave equation at the origin. A physical motivation is to replace the zero radius flux tube by one of radius R, with the additional condition that the magnetic field be confined to the surface of the tube, and then taking the limit R → 0 at the end of the computations. We point that the invariant operator must contain the step function θ(r – R). Consequently, the problem becomes more complicated. In order to avoid this difficulty, we replace the radius R by ρ(t)R, where ρ(t) is a positive time-dependent function. Then at the end of calculations we take the limit R → 0. The qualitative properties for the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation satisfied by ρ(t), i.e., C > 0, C = 0, and C < 0. Following the C's values the spectrum of quantum states is discrete (C > 0) or continuous (C ≤ 0).

We calculate the eigenvalues and eigenvectors of a five-qubit isotropic Heisenberg model in an external magnetic field, and give analytical results for the concurrence of two nearest-neighbor qubits. A magnetic field can eliminate degeneration and change the ground state of the system. Therefore increasing the value of the magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic case.

The disentanglement evolution of bipartite spin-1/2 system coupled to a common surrounding XY chain in transverse fields at nonzero temperature is studied in this letter. The dynamical process of the entanglement is numerically and analytically investigated. We find that thermal effects can enhance disentanglement if the entangled initial state of the central spins does not in the decoherence free space. The critical phenomenon of quantum phase transitions reflected in the disentanglement can be washed out by the thermal effect eventually.

Based on entanglement swapping, a quantum key distribution (QKD) scheme is proposed. In this scheme, the secret keys are formed by comparing initial Bell states and outcomes of entanglement swapping. Moreover, all initial Bell states prepared by Alice and Bob are completely arbitrary. As the classical information exchanged between two parties is very little, this QKD scheme has a high efficiency. In addition, in order to prevent eavesdropping, decoy particles are used.

In this paper, we present a scheme for teleporting multi-qudit quantum state, from the sender Alice to the receiver Charlie via many controllers Bobs, whose control parameters are obtained using entanglement swapping of maximally d-dimensional EPR pair. In our scheme, Yang's qutrit controlled teleportation protocol [Commun. Theor. Phys. 49 (2008) 338] based on Bell-state entanglement swapping is generalized to the qudit case. The scheme of multi-qudit owns the advantage of having higher code capacity and better security than that of multi-qutrit.

We propose a scheme for generation of SU(2) coherent states for an atomic ensemble and a cavity mode. In the scheme a collection of two-level atoms resonantly interact with a single-mode quantized field. Under certain conditions, the system can evolve from a Fock state to a highly entangled SU(2) coherent state. The operation speed increases as the number of atoms increases, which is important in view of decoherence.

This paper investigates the generation and evolution of continuous-variable entanglement in an asymmetric coupled-quantum well (CQW) system. Our numerical results show that this CQW system can be regarded as a source of macroscopic entangled light over a wide range of initial states of the cavity field. This investigation can be used for achieving the macroscopic entangled light in the CQW solid-state medium, which is much more practical than that in an atomic medium because of its flexible design and the controllable interference strength.

We investigate the self-tapping phenomena for two weakly coupled Bose–Einstein condensates with a rapid periodic modulation of the atomic scattering length. By using an averaging method, the equations of motion of the slow dynamics are derived to analyze the self-trapping behavior. It is shown numerically that under certain conditions, an alternative self-trapping in either well appears.

It is well known that the Poincaré gauge theories of gravity do not have the structure of a standard gauge theory. Nevertheless, we show that a general form of action for the gravitational gauge fields in the gauge theory does possess local Poincaré invariance.

The Casimir energy of massive scalar field with hybrid (Dirichlet–Neumann) boundary condition is calculated. In order to regularize the model, the typical methods named as mode summation method and Green's function method are used respectively. It is found that the regularized zero-point energy density depends on the scalar field's mass. When the field is massless, the result is consistent with previous literatures.

Applying the fermions tunneling method, proposed by Kerner and Mann recently, we discuss the tunneling characteristics of Dirac particles from the stationary Kaluza–Klein black hole. To choose Gamma matrix conveniently and avoid the ergosphere dragging effect, we perform it in the dragging coordinate frame. The result shows that Hawking temperature in this case also can be reproduced by the general Dirac equation.

In the paper, we study a super-conducting junctions device subject to an input periodic signal and a constant force. It is shown that, for this device, we can get current reversals for the current of the electron pairs versus the frequency of the periodic signal and negative conductance for the current of the electron pairs as a function of the constant force.

A family of coupled map lattice (CML) models has been developed to simulate the evolutional mechanism of interactions of convection, diffusion, and dispersion in both weakly and strongly coupled cases. Not only coherent and turbulent properties as well as their relations, but also the transitional states between convection dominating, diffusion dominating and dispersion dominating are analyzed to demonstrate the essential characteristics of any state. Numerical results show that the models are capable of simulating both layered coupling and stochastic mechanism, and lead us to understand whether or not turbulence coherent structure is formed by modulation of wave packet. The duality of wave and particle characters of turbulence is illustrated in the numerical simulation; a sketch picture is given to explain the questions associated with the turbulent inverse cascade, which is the result of the mutual interactions among the physical factors of nonlinearity, dissipation and dispersion.

The dynamical behavior of the extended Duffing-Van der Pol oscillator is investigated numerically in detail. With the aid of some numerical simulation tools such as bifurcation diagrams and Poincaré maps, the different routes to chaos and various shapes of strange attractors are observed. To characterize chaotic behavior of this oscillator system, the spectrum of Lyapunov exponent and Lyapunov dimension are also employed.

Lorenz systems family unifying Lorenz system, Chen system and Lü system is a typical chaotic family. In this paper, we consider impulsive control Lorenz chaotic systems family with time-varying impulse intervals. By establishing an effective tool of a set of inequalities, we analyze the asymptotic stability of impulsive control Lorenz systems family and obtain some new less conservative conditions. Based on the stability analysis, we design a novel impulsive controller with time-varying impulse intervals. Illustrative examples are provided to show the feasibility and effectiveness of our method. The obtained results not only can be used to design impulsive control for Lorenz systems family, but also can be extended to other chaotic systems.

In this paper, we investigate symmetries of the new (4+1)-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries and some constructive methods to get some doubly periodic wave solutions and other solutions of the Fokas equation. In particular, some solitary wave solutions are also given.

In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin–Meshkov–Glick model: an interacting collective spin system without external magnetic field. It is shown that this model with integer-spin can exhibit a first-order quantum phase transition between different disordered phases, and more intriguingly, possesses a hidden supersymmetry at the critical point. However, for half-integer spin we predict another first-order quantum phase transition between two different long-range-ordered phases with a vanishing energy gap, which is induced by the destructive topological quantum interference between the intanton and anti-instanton tunneling paths and accompanies spontaneously breaking of supersymmetry at the same critical point. We also show that, when the total spin-value varies from half-integer to integer this model can exhibit an abrupt variation of Berry phase from π to zero.

By employing the perturbative QCD (pQCD) factorization approach, we calculate some important next-to-leading-order (NLO) contributions to the two-body charmless hadronic decays B⁺ → ρ⁺ η^(') and B⁰ → ρ⁰ (ω, ø)η^('), induced by the vertex QCD corrections, the quark-loops as well as the chromo-magnetic penguins. From the numerical results and phenomenological analysis we find that (a) for B^± → ρ^±η^(') (B⁰ → ρ⁰ (ω, ø)η^(') decays, the partial NLO contributions to branching ratios are small (large) in magnitude; and (b) the pQCD predictions for A_CP^dir(B^± → ρ^±η^(')) are consistent with the data, while the predicted A_CP(B⁰ → ρ⁰(ω)η^(')) are generally large in magnitude and could be tested by the forthcoming LHCb experiments.

The relativistic mean-field (RMF) theory is used to calculate the properties of A = 7–9 drip-line nuclei ⁷Li, ^7;9Be, ^8;9B, and ⁹C. Systematic deviations between experimental and theoretical binding energies are found. Possible reasons of these systematic deviations are discussed in terms of pairing energy. The root-mean-square (rms) radii of matter distributions for these nuclei agree with the experimental data quite well. The one-proton halo structure in ⁸B is reproduced well, and the two-proton halo in ⁹ C is predicted. The calculations show that the RMF theory is valid in studying the properties of light drip-line nuclei.

The shell model calculations in the sdgh major shell for the neutron-deficient ¹⁰⁶,¹⁰⁷,¹⁰⁸,¹⁰⁹Sn isotopes have been carried out by using CD-Bonn and Nijmegen1 two-body effective nucleon-nucleon interactions. The single-shell states and the corresponding matrix elements needed for describing Sn isotopes are reconstructed to calculate the coefficient of fractional parantage by reducing the calculation requirements. This reconstruction allows us to do the shell model calculations of the neutron deficient Sn isotopes in very reasonable time. The results are compared to the recent high-resolution experimental data and found to be in good agreement with experiments.

The phonon and thermodynamics properties of face-centered cubic CaF₂ at high pressure and high temperature are investigated by using the shell model interatomic pair potential within General Utility Lattice Program (GULP). The phonon dispersion curves and the corresponding density of state (PDOS) in this work are consistent with the experimental data and other theoretical results. The transverse optical (TO) and longitudinal optical (LO) mode splitting as well as heat capacity at constant volume CV and entropy S versus pressure and temperature are also obtained.

The sixth-order accurate phase error flux-corrected transport numerical algorithm is introduced, and used to simulate Kelvin–Helmholtz instability. Linear growth rates of the simulation agree with the linear theories of Kelvin–Helmholtz instability. It indicates the validity and accuracy of this simulation method. The method also has good capturing ability of the instability interface deformation.

With the strong-field scheme and trigonal bases, the complete d³ energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the energy spectrum of YGG:Cr³⁺ at normal pressure and low temperature has been calculated. The g factor of the ground-state has been evaluated in terms of the energy spectrum. At the same time, by using the wavefunctions obtained from diagonalizing the complete d³ energy matrix and Thermal Shifts theory, we calculate the thermal shifts of the sharp lines of YGG:Cr³⁺ and determine the relevant parameters. The calculated results are all in good agreement with the optical-spectrum and EPR experimental data. It is demonstrated that the obtained wavefunctions and the values of parameters are reasonable.

Using the method of matrix diagonalization, we investigate an off-center D⁻ in a spherical quantum dot (QD) subjected to a parabolic potential confinement. We discuss the effect of the position of an impurity in the QD on the binding energy of the D⁻ system. Furthermore, we compare a negatively charged donor D⁻ with a neutral donor D⁰ confined by a spherical QD with a parabolic potential. The results have clearly demonstrate the so-called quantum size effect. The binding energy is dependent on the confining potential ħωø₀ and the impurity ion distance D.

The linear and nonlinear optical properties of a hydrogenic donor in a disc-like parabolic quantum dot in the presence of an external magnetic field are studied. The calculations were performed within the effective mass approximation, using the matrix diagonalization method and the compact density-matrix approach. The linear and nonlinear optical absorption coefficients between the ground (L = 0) and the first excited state (L = 1) have been examined based on the computed energies and wave functions. We find that the linear, nonlinear third-order, and total optical absorption coefficients are strongly affected by the confinement strength of QDs, the external magnetic field, and the incident optical intensity.

As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice (Z = 3). The Liapunov exponent λ is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude h₀/ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.

In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.

Using Langevin simulations, we investigate the depinning dynamics of two-dimensional charged colloids on a random laser-optical substrate. With an increase in the strength of the substrate, we find a transition from crystal to smectic flows above the depinning. A power-law scaling relationship between average velocity and applied driving force could be obtained for both flows, and we find that the scaling exponents are no bigger than 1 for the crystal and are bigger than 1 for the smectic flows.

Based on the Tang–Othmer Ca²⁺ model, the drift behavior of intracellular Ca²⁺ spiral waves under the influence of weak electric field is investigated. Numerical results show that the dependence of drift velocity of the spiral tip on dc electric field is similar to experimental observations in BZ system. When an ac electric field is applied, interesting resonant-drift phenomenon is observed with ω = 2Ω₀. All results can be explained analytically using a proximate method.

For most networks, the weight of connection is changing with their attachment and inner affinity. By introducing a mixed mechanism of weighted-driven and inner selection, the model exhibits wide range power-law distributions of node strength and edge weight, and the exponent can be adjusted by not only the parameter δ but also the probability q. Furthermore, we investigate the weighted average shortest distance, clustering coefficient, and the correlation of our network. In addition, the weighted assortativity coefficient which characterizes important information of weighted topological networks has been discussed, but the variation of coefficients is much smaller than the former researches.

The constraint on the total energy in a given spatial region is given from holography by the mass of a black hole that just fits in that region, which leads to an UV/IR relation: the maximal energy density in that region is proportional to M_p²/L², where M_p is the Planck mass and L is the spatial scale of that region under consideration. Assuming the maximal black hole in the universe is formed through gravitational collapse of perturbations in the universe, then the "Jeans" scale of the perturbations gives a causal connection scale R_CC. For gravitational perturbations, R_CC⁻² = Max ( + 2H², −) for a flat universe. We study the cosmological dynamics of the corresponding vacuum energy density by choosing the causal connection scale as the IR cutoff in the UV/IR relation, in the cases of the vacuum energy density as an independently conserved energy component and an effective dynamical cosmological constant, respectively. It turns out that only the case with the choice R⁻²_CC –2 = + 2H², could be consistent with the current cosmological observations when the vacuum density appears as an independently conserved energy component. In this case, the model is called holographic Ricci scalar dark energy model in the literature.