Table of contents

For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first, the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of non-Noether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.

Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differential equations of motion of the system are established. The definition and criterion of the form invariance of the system under infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-Noether conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describe self-similar solutions of plane curve motions in centro-affine and affine geometries.

New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breaking soliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutions and triangular periodic wave solutions are obtained.

In 3-mode Fock space we find a new tripartite entangled state |α,γ⟩_λ, which make up a new quantum mechanical representation. The state |α,γ⟩_λ can be generated by using the setup composing of a beam splitter and a parametric down-conversion amplifier. Application of the state is briefly discussed.

We study the entanglement of the superconducting charge qubit with the quantized electromagnetic field in a microwave cavity. It can be controlled dynamically by a classical external field threading the SQUID within the charge qubit. Utilizing the controllable quantum entanglement, we can demonstrate the dynamic process of the quantum storage of information carried by charge qubit. On the other hand, based on this engineered quantum entanglement, we can also demonstrate a progressive decoherence of charge qubit with quantum jump due to the coupling with the cavity field in quasi-classical state.

Tunneling dynamics of multi-atomic molecules between any two multi-atomic molecular Bose–Einstein condensates with Feshbach resonance is investigated. It is indicated that the tunneling in the two Bose–Einstein condensates depends not only on the inter-molecular nonlinear interactions and the initial number of molecule in these condensates, but also on the tunneling coupling between them. It is discovered that besides oscillating tunneling current between the multi-atomic molecular condensates, the nonlinear multi-atomic molecular tunneling dynamics sustains a self-locked population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence caused by non-condensate molecule on the tunneling dynamics is studied. It is shown that de-coherence suppresses the multi-atomic molecular tunneling.

The effective theory for the hierarchical fractional quantum Hall (FQH) effect is proposed. We also derive the topological numbers K matrix andt vector and the general edge excitation from the effective theory. One can find that the two issues in rapidly rotating ultracold atoms are similar to those in electron FQH liquid.

The directed motion of a Brownian particle in a flashing potential with various transition probabilities and waiting times in one of two states is studied. An expression for the average cycle period is proposed and the steady current J of the particle is calculated via Langevin simulation. The results show that the optimal cycle period τ_m, which takes the maximum of J, is shifted to a small value when the transition probability λ from the potential on to the potential off decreases, the maximal current appears in the case of the average waiting time in the potential on being longer than in the potential off, and the direction of current depends on the ratio of the average times waiting in two states.

A linear array of N mutually coupled single-mode lasers is investigated. It is shown that the intensities of N lasers are chaotically synchronized when the coupling between lasers is relatively strong. The chaotic synchronization of intensities depends on the location of the lasers in the array. The chaotic synchronization appears between two outmost lasers, the second two outmost lasers, etc. There is no synchronization between nearest neighbors of the lasers. If the number of N is odd, the middle laser is never synchronized between any lasers. The chaotic synchronization of phases between nearest lasers in the array is examined by using the analytic signal and the Gaussian filter methods based on the peak of the power spectrum of the intensity. It can be seen that the message of chaotic intensity synchronization is conveyed through the phase synchronization.

Some new exact travelling wave and period solutions of discrete nonlinear Schrödinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.

With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc. are revealed by selecting appropriate functions in this paper.

Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+1)-dimensional Broer–Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.

We investigate in detail the effects of R-parity lepton number violation on the decay ₁→b⁰₁ in the R-parity violating minimal supersymmetric standard model (/R_p-MSSM) under the present experimental constraints on /R_p parameters. In our numerical calculations we consider two cases of input parameters of the squark and slepton sectors, M_squark<M_slepton and M_squark>M_slepton, for comparison. The results show that the relative R-parity violating correction is not very sensitive to the mass of the lightest neutralino ⁰₁ and the degenerate R-parity violating coupling parameter λ'₂, but strongly depends on M_squark, M_slepton, tan β and the degenerate R-parity violating coupling parameter λ'₁. The relative correction is about −4∼3% and can exceed −6% in some region of parameter space. Therefore, precise experiment analyses on the decay ₁→b⁰₁ may provide a probe of the R-parity violation.

The pole position of the σ meson is determined using the recently proposed new unitarization method combined with the two-loop SU(2)×SU(2) chiral perturbation theory results. The scattering length parameters and the effective range parameters predicted by our method are in good agreement with experimental results. It is found that M_σ = 542±26±39 MeV, Γ_σ = 546±122±25 MeV.

We try to apply a constituent quark model (a variety chiral constituent quark model) and the resonating group approach for the multi-quark problems to compute the effective potential between the N in S-wave (the quarks in the nucleons N and , and the two nucleons relatively as well, are in S wave) so as to see the possibility if there may be a tight bound state of six quarks as indicated by a strong enhancement at threshold of p in J/ψ and B decays. The effective potential which we obtain in terms of the model and approach shows if the experimental enhancement is really caused by a tight S-wave bound state of six quarks, then the quantum number of the bound state is very likely to be I = 1,J^PC = 0⁻⁺.

An approximation method based on Regge behavior is presented. This new method relates the reduced cross section derivative and the structure function Regge behavior at low x. With the use of this approximation method, the C and λ parameters are calculated from the HERA reduced cross section data taken at low-x. Also, we calculate the structure functions F₂(x,Q²) even for low-x values, which have not been investigated. To test the validity of calculated structure functions, we find the gluon distribution function in the Leading order approximation based on Regge behaviour of structure function and compare to the NLO QCD fit to H1 data and NLO parton distribution function.

The experimental large fluctuation in odd-even differences in moments of inertia of deformed actinide nuclei is investigated using the particle-number conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. PNC calculations show that the large odd-even difference in moments of inertia mainly comes from the interference contributions j(μν) from particles in high j intruder orbitals μ and ν quite near the Fermi surface, which have no counterpart in the BCS formalism. The effective monopole and quadrupole pairing interaction strengths are determined to fit the experimental odd-even differences in binding energies and bandhead moments of inertia. The experimental results for the variation of moments of inertia with rotational frequency ω are reproduced well by the PNC calculation. The nearly identical experimental moments of inertia between ²³⁶U(gsb) and ²³⁸U(gsb) at low frequencies ℏω⩽0.20 MeV are also reproduced quite well.

Properties of the superdeformed bands of odd-odd nuclei in A ∼ 80 mass region are investigated systematically within the supersymmetry scheme including many-body interactions and a perturbation possessing the SO(5) (or SU(5)) symmetry on the rotational symmetry. The obtained γ-ray energies, and the dynamical moments of inertia agree with experimental data. It shows that this approach is quite powerful in describing odd-odd nuclei in A ∼ 80 mass region.

The probability of ⁵He particle emission has been affirmed theoretically [J.S. Zhang, Science in China G47 (2004) 137]. In order to describe the ⁵He emission, the theoretical formula of the double-differential cross section of emitted ⁵He is to be established. Based on the pick-up mechanism, used for calculating the formula of d, t, ³He, α emissions, the theoretical formula of double-differential cross section of ⁵He is obtained, which is expressed in the form of Legendre coefficients. In the case of low incident energies, the configuration [J.S. Zhang, Science in China G47 (2004) 137; J.S. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 83] is the dominant part in the reaction processes. The calculated result indicates that the forward peaked angular distribution of the composite particle emission is weaker than that of the emitted single nucleon due to pick-up nucleon from the Fermi sea. As an example, the reactions of n+¹⁴N have been calculated, and the Legendre coefficients of d, t, ³He, α, ⁵He emissions are obtained respectively. The results show that the forward tendency is decided by the average momentum per nucleon in the emitted composite particles. The larger the average momentum is, the stronger the forward tendency is.

The nonrelativistic dipole-length, -velocity and -acceleration absorption oscillator strengths for the 1s²2s–1s²2p transitions of the lithium isoelectronic sequence from Z = 11 to 20 are calculated by using the energies and the multiconfiguration interaction wave functions obtained from a full core plus correlation (FCPC) method. In most cases, the agreement between the oscillator strengths values from the length and velocity formula is up to four or five digit. Our results are also in good agreement with previous theoretical data available in the literature.

A complex optical model potential correlated by the concept of bonded atom, which considers the overlapping effect of electron clouds between two atoms in a molecule, is firstly employed to calculate the total cross sections for electron scattering on several molecules (NH₃, H₂O, CH₄, CO, N₂, O₂, and C₂H₄) over the energy range 10∼5000 eV using the additivity rule model at Hartree–Fock level. The difference between the bonded atom and the free one in states is that the overlapping effect of electron clouds of bonded atoms in a molecule is considered. The quantitative total cross sections are compared with the experimental data and with the other calculations wherever available and good agreement is obtained over the energy range 10∼5000 eV. It is shown that the correlated calculations are much closer to the available experimental data than the uncorrelated ones at lower energies, especially below 500 eV. Therefore, considering the overlapping effect of electron clouds in the complex optical model potential could be helpful for the better accuracy of the total cross section calculations of electron scattering from molecules.

A robust scheme is proposed for producing maximally entangled states for many trapped ions in thermal motion. In the scheme the ions are simultaneously illuminated by two standing-wave laser fields. During the operation the phases of the lasers are inverted, which not only cancels the vibration-dependent parts in the evolution operator, but also suppresses direct off-resonant coupling of the internal states. Thus, our scheme allows the production of entanglement for hot trapped ions with laser fields of high intensity, which makes the entanglement speed extremely high.

We derive the analytical expression of microcavity-enhanced factor for third harmonic generation in terms of detunings, linewidths, and the Purcell factors of the relevant microcavity modes. It is suitable for microcavities with any dimensions and arbitrary geometric shapes.

A modified cellular automaton model for traffic flow on highway is proposed with a novel concept about the variable security gap. The concept is first introduced into the original Nagel–Schreckenberg model, which is called the non-sensitive driving cellular automaton model. And then it is incorporated with a sensitive driving NaSch model, in which the randomization brake is arranged before the deterministic deceleration. A parameter related to the variable security gap is determined through simulation. Comparison of the simulation results indicates that the variable security gap has different influence on the two models. The fundamental diagram obtained by simulation with the modified sensitive driving NaSch model shows that the maximum flow are in good agreement with the observed data, indicating that the presented model is more reasonable and realistic.

Kinetic Alfvén Wave (KAW) is one of the low-frequency electromagnetic fluctuations that are identified extensively in space plasmas by in situ observations of satellites and has been an interesting topic for discussion widely in the fields of laboratory, space, and astrophysical plasmas because of its potential importance in plasma particle energization. Some satellite observations show that the number density ratio of the oxygen ions to the ambient plasma is 30% ∼ 50%, sometimes, even as high as 80%. In this paper, effects of heavy ion species on KAWs are studied in a low-beta plasma. The results show that heavy ions not only considerably reduce the propagation speed of KAWs, but also remarkably influence the parallel component of perturbed electric field of KAWs (to the ambient magnetic field). The ratio of parallel to perpendicular components of perturbed field decreases (or increases) with the heavy ion abundance for KAWs dominated by the electron inertial length (or by ion acoustic gyroradius). In particular, the resonant condition of KAWs with thermal electrons is modified by the heavy ion species.

The dispersions of the top interface optical phonons and the side interface optical phonons in cylindrical quantum dots are solved by using the dielectric continuum model. Our calculation mainly focuses on the frequency dependence of the IO phonon modes on the wave-vector and quantum number in the cylindrical quantum dot system. Results reveal that the frequency of top interface optical phonon sensitively depends on the discrete wave-vector in z direction and the azimuthal quantum number, while that of the side interface optical phonon mode depends on the radial and azimuthal quantum numbers. These features are obviously different from those in quantum well, quantum well wire, and spherical quantum dot systems. The limited frequencies of interface optical modes for the large wave-vector or quantum number approach two certain constant values, and the math and physical reasons for this feature have been explained reasonably.

The electron paramagnetic resonance (EPR) parameters (zero-field splitting D and g factors g_∥, g_⊥) of Cr⁴⁺ ions in Ca₂GeO₄ crystals have been calculated from the complete high-order perturbation formulas of EPR parameters for a 3d² ion in trigonal MX₄ clusters. In these formulas, in addition to the contributions to EPR parameters from the widely used crystal-field (CF) mechanism, the contributions from the charge-transfer (CT) mechanism (which are often neglected) are included. From the calculations, it is found that for the high valence state 3dⁿ ions in crystals, the reasonable explanation of EPR parameters (in particular, the g factors) should take both the CF and CT mechanisms into account.

We investigate the linear and nonlinear transport through a single level quantum dot connected to two ferromagnetic leads in Kondo regime, using the slave-boson mean-field approach for finite on-site Coulomb repulsion. We find that for antiparallel alignment of the spin orientations in the leads, a single zero-bias Kondo peak always appears in the voltage-dependent differential conductance with peak height going down to zero as the polarization grows to P = 1. For parallel configuration, with increasing polarization from zero, the Kondo peak descends and greatly widens with the appearance of shoulders, and finally splits into two peaks on both sides of the bias voltage around P∼0.7 until disappearing at even larger polarization strength. At any spin orientation angle θ, the linear conductance generally drops with growing polarization strength. For a given finite polarization, the minimum linear conductance always appears at θ = π.

The compound {[Cu(Hpht)(N₃)]·H₂O}_n (Hpht = hydrogen phthalate) is formed by chains of copper atoms bridged simultaneously by syn-syn carboxylato and end-on azido bridges. Taking into account the large Cu-O(1)-C(7) bond angle of the single carboxylato bridge (131°), or the large Cu-N(11)-Cu bond angle of the azido bridge (111.9°), a moderately intrachain antiferromagnetic behavior should be expected for the compound. This paper is devoted to examining the apparently anomalous intrachain ferromagnetic behavior of {[Cu(Hpht)(N₃)]·H₂O}_n, using first principles within the full potential linearized augmented plane wave (FP-LAPW) method. The total energy, the density of states (DOS), and the spin distributions are obtained. The atomic spin distribution has been analyzed as resulting from the interplay of electron delocalization and spin polarization. The DOS reveals a surprisingly strong exchange interaction between the d type orbitals of the copper and the π molecular orbitals of the two ligands.

In this letter, we have studied the influence of the external magnetic fields on tunneling of the spin-1 Bose condensate. We find that the population transfer between spin-0 and spin-±1 exhibits the step structure under the external cosinusoidal magnetic field and a combination of static and cosinusoidal one, respectively. Compared with the longitudinal component of the external magnetic field, the smaller the transverse component of the magnetic field is, the larger the time scale of exhibiting the step structure does. The tunneling current may exhibit periodically oscillation behavior when the ratio of the transverse component of the magnetic field is smaller than that of the longitudinal component, otherwise it exhibits a damply oscillating behavior. This means that the dynamical spin localization can be adjusted by the external magnetic fields.

A variational approach is developed to study the groundstate (GS) of the two-site Holstein model. By the extended coherent state, where the more phonon correlations are easily incorporated, we can get the very accurate ground state energy for all electron-phonon coupling range in typical values of hopping integral t = 0.5,1.1, and 2.1 (in units of phonon frequency ω₀), which covers the crossover region from antiadiabatic limit to the adiabatic limit. Within a very wide t range [0,2.7], the exact results for the GS energy are obtained with the twelfth (fourteenth) order corrections to the zeroth order wave function. Moreover, the present approach is more concise than any other analytical ones in this field, and hopefully can be easily generalized to many other Holstein models.

Ferroelectric phase diagrams and the temperature dependence of polarization, dielectric properties of the three pseudo-spin in ferroelectric or ferro-antiferroelectric system described by a transverse Ising models are investigated on the basis of the effective-field theory with the differential operator technique. The effects of the transverse field and the coupling strength between the nearest-neighboring pseudo-spin on the physical properties are discussed in detail.

Utilizing the improved model with quasi-coherent two-quantum state and new Hamiltonian containing an additional interaction term [Phys. Rev. E62 (2000) 6989 and Euro. Phys. J. B19 (2001) 297] we study numerically the influences of the quantum and disorder effects including distortion of the sequences of masses of amino acid molecules and fluctuations of force constant of molecular chains, and of exciton-phonon coupled constants and of the dipole-dipole interaction constant and of the ground state energy on the properties of the solitons transported the bio-energy in the protein molecules by Runge–Kutta method. The results obtained show that the new soliton is robust against these structure disorders, especially for stronger disorders in the sequence of masses spring constants and coupling constants, except for quite larger fluctuations of the ground state energy and dipole-dipole interaction constant. This means that the new soliton in the improved model is very stable in normal cases and is possibly a carrier of bio-energy transport in the protein molecules.

We study force generation and motion of molecular motors using a simple two-state model in the paper. Asymmetric and periodic potential is adopted to describe the interaction between motor proteins and filaments that are periodic and polar. The current and the slope of the effective potential as functions of the temperature and transition rates are calculated in the two-state model. The ratio of the slope of the effective potential to the current is also calculated. It is shown that the directed motion of motor proteins is relevant to the effective potential. The slope of the effective potential corresponds to an average force. The non-vanishing force therefore implies that detailed balance is broken in the process of transition between different states.

Using the generalized uncertainty relation, the new equation of state density is obtained, and then the entropy of black hole with an internal global monopole is discussed. The divergence that appears in black hole entropy calculation through original brick-wall model is overcome. The result of the direct proportion between black hole entropy and its event horizon area is drawn and given. The result shows that the black hole entropy must be the entropy of quantum state near the event horizon.