Table of contents

We analyze in detail the quantum phase transitions that arise in models based on the u(2) algebraic description for bosonic systems with two types of scalar bosons. First we discuss the quantum phase transition that occurs in hamiltonians that admix the two dynamical symmetry chains u(2)⊃ u(1) and u(2) ⊃so(2) by diagonalizing the problem exactly in the u(1) basis. Then we apply the coherent state formalism to determine the energy functional. Finally we show that a quantum phase transition of a different nature, but displaying similar characteristics, may arise also within a single chain just by including higher order terms in the hamiltonian.

With the help of the zero-curvature equation and the super trace identity, we derive a super extension of the Kaup—Newell hierarchy associated with a 3 × 3 matrix spectral problem and establish its super bi-Hamiltonian structures. Furthermore, infinite conservation laws of the super Kaup—Newell equation are obtained by using spectral parameter expansions.

Based on a transformed Painlevé property and the variable separated ODE method, a function transformation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painlevé property and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions to the resulting equations by some methods. As an application, exact solutions for the combined sinh-cosh-Gordon equation are formally derived.

In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov—Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.

We propose a method to construct the integrable Rosochatius deformations for an integrable couplings equations hierarchy. As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy with self-consistent sources and its Lax representation are presented.

Soliton theory plays an important role in nonlinear physics. The elastic interaction among solitons is one of the most important properties for integrable systems. In this Letter, an elastic vortex interaction model is proposed. It is found that the momenta, vortex momenta and the energies of every one vortex and the interaction energies of every two vortices are conserved.

The Rosochatius system on the sphere, an integrable mechanical system discovered in the nineteenth century, is investigated in a suitably chosen framework with the sphere as an invariant set, to avoid the complicated constraint presentations. Higher order Rosochatius flows are defined and straightened out in the Jacobi variety of the associated hyperelliptic curve. A relation is found between these flows and the KdV equation, whose finite genus solution is calculated in the context of the Rosochatius hierarchy.

Two spherically symmetric non-singular black hole solutions in Möller tetrad theory of gravitation have been obtained. Although the two solutions have the same form of metric (spherically symmetric nonsingular black hole), their energy contents are different. We use another method given by Gibbons and Hawking to calculate the energy content of these solutions. We also obtained different value of energy. Study the requirements of a satisfactory energy-momentum complex given by Möller we find that the second solution, which behaves as , is not transformed as a four-vector under Lorentz transformation.

F₁-ATPase, a part of ATP synthase, can synthesize and hydrolyze ATP moleculars in which the central γ-subunit rotates inside the α₃ β₃cylinder. A stochastic four-state mechanochemical coupling model of F₁-ATPase is studied with the aid of the master equation. In this model, the ATP hydrolysis and synthesis are dependent on ATP, ADP, and Pi concentrations. The effects of ATP concentration, ADP concentration, and the external torque on the occupation probability of binding-state, the rotation rate and the diffusion coefficient of F₁-ATPase are investigated. Moreover, the results from this model are compared with experiments. The mechanochemical mechanism F₁-ATPase is qualitatively explained by the model.

Investigated in this paper is the generalized nonlinear Schrödinger equation with radial symmetry. With the help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear method. Bäcklund transformation in the bilinear form is presented, through which a new solution is constructed. Graphically, we have found that the solitons are symmetric about x=0, while the soliton pulse width and amplitude will change along with the distance and time during the propagation.

Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity. Though this is a beautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many other problems. In this article I will comment on some of the problems of Verlinde's proposal with special emphasis on the thermodynamical origin of the principle of relativity. It is found that there is a large group of hidden symmetries of thermodynamics, which contains the Poincare group of the spacetime for which space is emergent. This explains the thermodynamic origin of the principle of relativity.

We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one component associated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.

By virtue of the normal ordering of vacuum projector we directly derive some new complicated operator identities, regarding to the generalized Stirling number.

The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KS transformation.

The unified bound on the fundamental limit of quantum dynamics rate, as quietly recently obtained by Levitin and Toffoli [Phys. Rev. Lett. 103 (2009) 160502], is improved and refined. The improvement may be arbitrarily large in certain cases. In particular, this puts a limit on the operation rate of quantum gates allowed by quantum mechanics.

Based on the ground states of the one-dimensional Lipkin—Meshkov—Glick model (LMGM), we show an all-versus-nothing proof of violation of local realism in this model. Moreover, the quantum entanglement swapping is also investigated in terms of the braiding transformations.

The entanglement characteristics including the so-called sudden death effect between two identical two-level atoms trapped in two separate cavities connected by an optical fiber are studied. The results show that the time evolution of entanglement is sensitive not only to the degree of entanglement of the initial state but also to the ratio between cavity-fiber coupling (v) and atom-cavity coupling (g). This means that the entanglement dynamics can be controlled by choosing specific v and g.

We introduce the double-Hamiltonian evolution technique approach to investigate the unconventional geometric quantum logical gate with dissipation under the model of many identical three-level atoms in a cavity, driven by a classical field. Our concrete calculation is made for the case of two atoms for the large-detuning interaction of the atoms with the cavity mode. The main advantage of our scheme is of eliminating the photon flutuation in the cavity mode during the gating. The corresponding analytical results will be helpful for experimental realization of speed geometric quantum logical gate in real cavities.

In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times.

This paper concerns with the master-slave exponential synchronization analysis for a class of general Lur'e systems with time delay. Different from the previous methods based on the differential inequality technique, a new approach is proposed to derive some new exponential synchronization criteria. The restriction that the control width has to be larger than the time delay is removed. This leads to a larger application scope for our method. Moreover, no transcendental equation is involved in the obtained result, which reduces the computational burden. Two examples are given to validate the theoretical results.

Under investigation in this paper are two coupled integrable dispersionless (CID) equations modeling the dynamics of the current-fed string within an external magnetic field. Through a set of the dependent variable transformations, the bilinear forms for the CID equations are derived. Based on the Hirota method and symbolic computation, the analytic N-soliton solutions are presented. Infinitely many conservation laws for the CID equations are given through the known spectral problem. Propagation characteristics and interaction behaviors of the solitons are analyzed graphically.

The axial charges of the proton and N(1440) are studied in the framework of an extended constituent quark model (CQM) including qqqq components. The cancellation between the contributions of qqq components and qqqq components gives a natural explanation to the experimental value of the proton axial charge, which can not be well reproduced in the traditional CQM even after the SU(6) ⊗ O(3) symmetry breaking is taken into account. The experimental value of axial charge pins down the proportion of the qqqq component in the proton to about 20%, which is consistent with the ones given by the strong decay widths and helicity amplitudes. Besides, an axial charge for N(1440) about 1 is predicted with 30% qqqq component, which is obtained by the strong and electromagnetic decays.

The left-right twin Higgs (LRTH) model predicts the existence of three additional Higgs bosons: one neutral Higgs φ⁰ and a pair of charged Higgs bosons φ^±. In this paper, we study two pair production processes of these new particles at the next generation eγ colliders, i.e., e⁻γ→ e⁻φ⁺φ⁻, and e⁻γ→ ν_Rφ⁻φ⁰. We find that the production cross section of the process e⁻γ→ e⁻φ⁺φ⁻ are at the level of several tens fb, the production cross section of the process e⁻γ→ ν_Rφ⁻φ⁰ can reach 0.35 fb with the reasonable parameter values. As long as the charged Higgs bosons are not too heavy, we conclude that these processes might be used to test for the left-right twin Higgs model in future high-energy linear collider experiments.

The SO(3) gauge extension of SM, which is proposed to present a successful explanation for the observed small masses of neutrino and the nearly tri-bimaximal neutrino mixing, predicted the vector-like SO(3) triplet Majorana neutrinos and SU_L(2) double Higgs bosons. In this work we calculate branching ratios of the charged lepton flavor violating decays induced by these Majorana neutrinos and Higgs bosons. We find that under the model parameters constrained by experimental bounds on the decays , the branching ratio of decays ℓ_I→ℓ_Jγ can be up to 10⁻¹⁰, which may be accessible at the future experiments.

Deexcitation energies of superdeformed secondary minima of odd-odd Au and Tl isotopes are investigated with the relativistic mean field (RMF) model where the isoscalar-isovector coupling is included to change the symmetry energy. It is verified by the theoretical analysis and numerical results that the deexcitation energies of superdeformed secondary minima relative to the ground states in these heavy nuclei are sensitive to differences in the symmetry energy. In particular, the linear correlation between the deexcitation energies of odd-odd Au and Tl isotopes and the neutron skin thickness in ²⁰⁸Pb is established. Moreover, explorations are extended to superdeformed candidates of other mass regions. It is found that the linear correlation can even be established between the deexcitation energies and the symmetry pressure at subsaturation density. These indicate that deexcitation energies can serve as a probe to the density dependence of the symmetry energy.

Using a first-principle method, the electronic structures and the impurity formation energy of ZnO, ZnO (N), ZnO (N+B), and ZnO (2N+B) have been calculated, based on which the feasibility to obtain p-type ZnO is discussed. According to the results, when ZnO is single doped by N, the acceptor level is deep, and the formation energy is negative, so the ideal p-type ZnO can not be obtained by this way. On the contrary, when 2N+B are codoped into ZnO, the acceptor level becomes much lower, and the formation energy is positive, so it is a better way to obtain p-type ZnO.

The dynamics of different kinds of discrete breathers in three types of one-dimensional monatomic chains with on-site and inter-site potentials are investigated. The existence and evolution of symmetric breather, antisymmetric breather, and multibreather in one-dimensional models are proved by using rotating wave approximation, local anharmonic approximation, and the numerical method. The linear stability of these breathers is investigated by using Lyapunov stable analysis. The localization and stability of breathers in three types of models correlate closely to the system nonlinear parameter β.

In this paper, we developed a new parametrization method to calculate the localization length in one-dimensional Anderson model with diagonal disorder. This method can avoid the divergence difficulty encountered in the conventional methods, and significantly save computing time as well.

Charge carriers in organic semiconductor are different from that of traditional inorganic semiconductor. Based on three-current model, considering electrical field effect, we present a theoretical model to discuss spin-polarized injection from ferromagnetic electrode into organic semiconductor by analyzing electrochemical potential both in ferromagnetic electrode and organic semiconductors. The calculated result of this model shows effects of electrode's spin polarization, equilibrium value of polarons ratio, interfacial conductance, bulk conductivity of materials and electrical field. It is found that we could get decent spin polarization with common ferromagnetic electrode by increasing equilibrium value of polarons ratio. We also find that large and matched bulk conductivity of organic semiconductor and electrode, small spin-dependent interfacial conductance, and enough large electrical field are critical factors for increasing spin polarization.

In this paper, we apply the two-time Green's function method, and provide a simple way to study the magnetic properties of one-dimensional spin-(S,s) Heisenberg ferromagnets. The magnetic susceptibility and correlation functions are obtained by using the Tyablikov decoupling approximation. Our results show that the magnetic susceptibility and correlation length are a monotonically decreasing function of temperature regardless of the mixed spins. It is found that in the case of S=s, our results of one-dimensional mixed-spin model is reduced to be those of the isotropic ferromagnetic Heisenberg chain in the whole temperature region. Our results for the susceptibility are in agreement with those obtained by other theoretical approaches.

We study theoretically the possibility of superconductivity state in pure graphene within the extended attractive Hubbard model. In the absence of disorder, when we use the local attractive interaction potential, U ⋍ 5t, where t is hopping term, pure graphene can be in superconductivity state.

Based on the transverse Ising model and using decoupling approximation to the Fermi-type Green's function, we study the phase transition properties of the epitaxial ferroelectric film with one substrate. A general recursive equation of the ferroelectric thin film with two n-layer materials is obtained, which enables us to study the phase transition properties for any number layers for epitaxial ferroelectric thin film. With the help of this equation, we analyze the effect of the exchange interaction and the transverse field in the phase diagram, the influence to the polarizations and Curie temperature numerically. The results show that epitaxial ferroelectric film are able to induce a strong increase or decrease of Curie temperature to different exchange interactions and transverse fields within the epitaxial film layers. The theoretical results are in reasonable accordance with experimental data of different ferroelectric thin film.

As the channel length of metal-oxide-semiconductor field-effect transistors (MOSFETs) scales into the nanometer regime, quantum mechanical effects are becoming more and more significant. In this work, a model for the surrounding-gate (SG) nMOSFET is developed. The Schrödinger equation is solved analytically. Some of the solutions are verified via results obtained from simulations. It is found that the percentage of the electrons with lighter conductivity mass increases as the silicon body radius decreases, or as the gate voltage reduces, or as the temperature decreases. The centroid of inversion-layer is driven away from the silicon-oxide interface towards the silicon body, therefore the carriers will suffer less scattering from the interface and the electrons effective mobility of the SG nMOSFETs will be enhanced.

Multimotor transport is studied by Monte-Carlo simulation with consideration of motor detachment from the filament. Our work shows, in the case of low load, the velocity of multi-motor system can decrease or increase with increasing motor numbers depending on the single motor force-velocity curve. The stall force and run-length reduced greatly compared to other models. Especially in the case of low ATP concentrations, the stall force of multi motor transport even smaller than the single motor's stall force.

We study phantom-like effect on the DGP brane embedded in a five-dimensional AdS bulk. We show that this effect can be realized without phantom matter on this warped DGP brane. We investigate the role played by the bulk cosmological constant on the phantom-like effect on the brane and we show that it tends to reduce this effect. Also, warped compactification of the bulk manifold increases the values of the effective and total equation of state parameters of the model relative to the case with Minkowski bulk. We extend our study to the case that induced curvature on the brane is modified in the spirit of the f(R)-gravity.