Table of contents

Bosonization approach is applied in solving the most general N = 1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a (sKdV-a) equation. By introducing some fermionic parameters in the expansion of the superfield, the sKdV-a equation is transformed to a new coupled bosonic system. The Lie point symmetries of this model are considered and similarity reductions of it are conducted. Several types of similarity reduction solutions of the coupled bosonic equations are simply obtained for all values of a. Some kinds of exact solutions of the sKdV-a equation are discussed which was not considered integrable previously.

In this paper, the (G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann—Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota—Satsuma coupled KdV equations and the time-fractional fifth-order Sawada—Kotera equation. As a result, some new exact solutions for them are successfully established.

Based on the corresponding theorem between dispersionless KP (dKP) hierarchy and ħ-dependent KP (ħKP) hierarchy, a general formal representation of the recursion operators for dKP hierarchy under n-reduction is given in a systematical way from the corresponding ħKP hierarchy. To illustrate this method, the recursion operators for dKP hierarchy under 2-reduction and 3-reduction are calculated in detail.

We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave functions and the degree of degeneracy. By comparison, we refine Avinash Khare's results by making some items in his article precisely.

Asymptotic energy expansion method is extended for polynomial potentials having rational powers. New types of recurrence relations are derived for the potentials of the form V (x) = x^2n/m + b₁x^n1/m1 + b₂x^n2/m2 + ... + b_Nx^n_N/m_N where n, m, n₁, m₁, ..., n_N, m_N are positive integers while coefficients b_k ∈ . As in the case of even degree polynomial potentials with integer powers, all the integrals in the expansion can be evaluated analytically in terms of Γ functions. With the help of two examples, we demonstrate the usefulness of these expansions in getting analytic insight into the quantum systems having rational power polynomial potentials.

We study the influence of multi-photon processes on the geometric quantum computation in the systems of superconducting qubits based on the displacement-like and the general squeezed operator methods. As an example, we focus on the question about how to implement a two-qubit geometric phase gate using superconducting circuit quantum electrodynamics with both single- and two-photon interaction between the qubits and the cavity modes. We find that the multiphoton processes are not only controllable but also improve the gating speed. The comparison with other physical systems and experimental feasibility are discussed in detail.

The effects of the different Dzyaloshinskii—Moriya (DM) interaction on thermal entanglement of a two-qutrit Heisenberg XX spin chain in a nonuniform magnetic field are investigated. Our results imply that the x-component DM interaction plays a central role in enhancing quantum entanglement and it has a higher critical temperature than the z-component DM interaction. The entanglement can be tunable controlled by changing the multiple of the magnetic fields B₁ and B₂. Also we found that different DM interaction are competitive to each other in some conditions.

We investigate the evolution dynamics of a two-level atom system interacting with the massless scalar field in a Cylindrical spacetime. We find that both the energy shifts of ground state and excited state can be separated into two parts due to the vacuum fluctuations. One is the corresponding energy shift for a rest atom in four-dimensional Minkowski space without spatial compactification, the other is just the modification of the spatial compactified periodic length. It will reveal that the influence of the presence of one spatial compactified dimension can not be neglected in Lamb shift as the relative energy level shift of an atom.

We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes always allow error recovery if only one among the sent qubits is disturbed in the transmitting channel. However, if two qubits and more are disturbed, then the correction will depend on the used code. We compare in this paper the three codes by computing the average fidelity between the sent secret and that measured by the receivers. We will treat the case where, at most, two qubits are affected in each one of five depolarizing channels.

We analyze the ground-state properties and the excitation spectrum of Bose—Einstein condensates of photons and PPs in a two-dimensional optical microcavity. First, using the variational method, we discuss the ground-state phase transition of the two-component system. We also investigate the energy gap between the ground state and the first excited state. Moreover, by investigating the excitation spectrum, we also illustrate how the superfluid behavior of photons and PPs can be associated with the phase transition of the system.

We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.

This paper studies the exponential cluster synchronization in arrays of coupled discrete-time dynamical networks with time-varying delay, in which the hybrid coupling is involved. Through choosing two improved Lyapunov—Krasovskii functionals, some delay-dependent sufficient conditions are presented based on reciprocal convex technique and Kronecker product. These criteria are presented in terms of LMIs and their feasibility can be easily checked by resorting to Matlab LMI Toolbox. Moreover, the addressed system can include some famous network models as its special cases and the effective techniques are used, which can extend some earlier reported results. Finally, the effectiveness of the proposed methods can be further illustrated with the help of two numerical examples.

This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors. The two networks can be undirected or directed, and they may also contain isolated nodes and clusters. By using suitable controllers, sufficient conditions for finite-time generalized outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the synchronization time is also numerically demonstrated.

In this paper we will study non-abelian Chern—Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern—Simons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin—Vilkovisky (BV) formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.

The top triangle moose (TTM) model, which can be seen as the deconstructed version of the topcolor-assisted technicolor (TC2) model, predicts the existence of the charged top-pions π_t^± in low energy spectrum. In the context of this model, we consider photoproduction of π_t^± via the subprocesses γb → tπ_t⁻ and at the large hadron-electron collider (LHeC), in which high energy photon beams are generated by using the Compton backscatting method. We find that, as long as the charged top-pions are not too heavy, they can be abundantly produced via 76 collision.

Within the context of the Littlest Higgs model with T-parity, the heavy photon (A_H) is supposed to be an ideal dark matter (DM) candidate. One direct proof of validity of the model is to produce the heavy photon at collider. In this paper, we investigate the associated production of a photon with heavy photon pair at the planned international e⁺e⁻ linear collider (ILC), i.e., e⁺e⁻ → A_HA_Hγ and show the distributions of the transverse momenta of the photon. The numerical results indicate that the heavy photon production rate could reach several fb at the low mass parameter space and the characteristic signal is a single high energetic photon and missing energy, carried by the heavy photons. All in all, it can be a good chance to observe the heavy photon via this process with the high yearly luminosity of the ILC.

In this article, we study the (1/2)^± and (3/2)^± triply heavy baryon states in a systematic way by subtracting the contributions from the corresponding (1/2)^∓ and (3/2)^∓ triply heavy baryon states with the QCD sum rules, and make reasonable predictions for their masses.

To explain the anomalously large decay rate of Σ⁺ → p + μ⁺μ⁻, it was proposed that a new mechanism where a light CP-odd pseudoscalar boson of m_A⁰1 = 214.3 MeV makes a crucial contribution. Later, some authors have studied the transition π⁰ → e⁺e⁻ and ϒ → γA⁰₁ in terms of the same mechanism and their result indicates that with the suggested mass one cannot fit the data. This discrepancy might be caused by experimental error of Σ⁺ → p + μ⁺μ⁻ because there were only a few events. Whether the mechanism is a reasonable one motivates us to investigate the transitions π⁰ → e⁺e⁻; η(η') → μ⁺μ⁻; η_c → μ⁺μ⁻; η_b → τ⁺τ⁻ within the same framework. It is noted that for π⁰ → e⁺e⁻, the standard model (SM) prediction is smaller than the data, whereas the experimental central value of η → μ⁺μ⁻ is also above the SM prediction. It means that there should be extra contributions from other mechanisms and the contribution of A⁰₁ may be a possible one. Theoretically calculating the branching ratios of the concerned modes, we would check if we can obtain a universal mass for A⁰₁ which reconcile the theoretical predictions and data for all the modes. Unfortunately, we find that it is impossible to have such a mass with the same coupling |gℓ|. Therefore we conclude that the phenomenology does not favor such a light A⁰₁, even though a small window is still open.

In this study, the analytical solutions of the radial Schrödinger equation for the central Woods—Saxon potential together with spin-orbit interaction and centrifugal terms have been derived by using Nikiforov-Uvarov method. The energy eigenvalues and corresponding eigenfunctions of nucleons have been obtained for various values of n, l, and j quantum numbers. The obtained results using this method are in satisfactory agreement with available data in the special case.

In this paper a cellular automaton model is proposed to describe driver behavior at a single-lane urban roundabout. Driver behavior has been considered as heterogeneous and inconsistent. Most traffic papers in the literature just discussed heterogeneous driver behavior, to our best knowledge. Two truncated Gaussian distributions are used to model heterogeneous and inconsistent driver behavior, respectively. The physical meanings of two truncated distributions are indicated. This method may help enhance a better understanding of driver behavior at roundabout traffic, and even possibly provide references for roundabout design and management.

A new type of homoclinic and heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanical feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlinear evolution system. Moreover, the similarities and differences between homoclinic (heteroclinic) breather and homoclinic (heteroclinic) tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.

The ultracold polar molecules with the tunable dipole-dipole interaction, not only would enable explorations of a large class of exotic many-body physics phenomena, but also could be used for quantum information processing. In the present paper we demonstrate that this dipole-dipole interaction can generate the degenerate chiral quantum states acting as a qubit robust against noise when the ultracold polar molecules are confined by a triangular lattice. Moreover, we also find two first-order quantum phase transitions by controlling an external driving field. One is the transition with the change of the different degenerate chiral quantum states. The other is the transition with the breaking of the degenerate quantum chiral states to the nondegenerate state. In experiment, these first-order quantum phase transitions can be detected by measuring the collective molecular population.

In this work, thermodynamical properties of a two-dimensional (2D) Lennard—Jones (LJ) fluid are studied. Here, to increase the accuracy of our theoretical calculations, the correlation functions in three-particle level (triplet) are applied. To obtain the triplet correlation functions, the Attard's source particle method is extended to 2D systems. In the Attard's procedure, the inhomogeneous Ornstein—Zernike (OZ) equation is solved using the Treizenberg—Zwanzwig (TZ) expression and a closure relation like the hypernetted-chain (HNC) approximation. In the present work, we also have performed the Monte Carlo (MC) simulation. The theoretical results are in fairly agreement with the MC simulation. Also, our results show that the approach proposed here is suitable to study the 2D LJ fluid.

We investigate the guided modes in monolayer graphene-based waveguides with asymmetric quantum well structure induced by unequal dc voltages. The dispersion relation for the guided modes is obtained analytically, the structures of the guided modes are discussed under three distinct cases. For the cases of the classical motion and the Klein tunneling, the asymmetric structure does not influence the mode structures dramatically compared with that in the symmetric waveguide. But for the mixing case of the former two, the mode structures and the motion characteristics for the electron and the hole exhibit different behaviors at same condition. The results may be helpful for the practical application of graphene-based quantum devices.

The magnetic susceptibility of ternary metal Prussian blue analogues with orthorhombic structure is studied using Ising model. Within the frame work of effective-field theory with correlations, the roles of the mole fraction y, uniaxial magnetic anisotropy, transverse and longitudinal magnetic field are discussed in details. The temperature dependence of the magnetic susceptibility is also investigated. The interesting phenomenon of the inverted magnetic hysteresis loop has been found. The results can help to understand the experimental work of the molecule-based ferri-ferrimagnet.

We report the electronic band structure and optical parameters of X-Phosphides (X=B, Al, Ga, In) by first-principles technique based on a new approximation known as modified Becke—Johnson (mBJ). This potential is considered more accurate in elaborating excited states properties of insulators and semiconductors as compared to LDA and GGA. The present calculated band gaps values of BP, AlP, GaP, and InP are 1.867 eV, 2.268 eV, 2.090 eV, and 1.377 eV respectively, which are in close agreement to the experimental results. The band gap values trend in this study is as: E_g(mBJ-GGA/LDA) > E_g(GGA) > E_g(LDA). Optical parametric quantities (dielectric constant, refractive index, reflectivity and optical conductivity) which based on the band structure are also presented and discussed. BP, AlP, GaP, and InP have strong absorption in between the energy range 4–9 eV, 4–7 eV, 3–7 eV, and 2–7 eV respectively. Static dielectric constant, static refractive index and coefficient of reflectivity at zero frequency, within mBJ-GGA, are also calculated. BP, AlP, GaP, and InP show significant optical conductivity in the range 5.2–10 eV, 4.3–8 eV, 3.5–7.2 eV, and 3.2–8 eV respectively. The present study endorses that the said compounds can be used in opto-electronic applications, for different energy ranges.