Table of contents

Burgers equation is the simplest one in soliton theory, which has been widely applied in almost all the physical branches. In this paper, we discuss the Painlevé property of the (3+1)-dimensional Burgers equation, and then Bäcklund transformation is derived according to the truncated expansion of the obtained Painlevé analysis. Using the Bäcklund transformation, we find the rouge wave solutions to the equation via the multilinear variable separation approach. And we also give an exact solution obtained by general variable separation approach, which is proved to possess abundant structures.

In this article, we propose an alternative approach of the generalized and improved (G'/G)-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti—Leon—Pempinelle equation, the Pochhammer—Chree equations and the Painleve integrable Burgers equation with free parameters. When the free parameters receive particular values, solitary wave solutions are constructed from the traveling waves. We use the Jacobi elliptic equation as an auxiliary equation in place of the second order linear equation. It is established that the proposed algorithm offers a further influential mathematical tool for constructing exact solutions of nonlinear evolution equations.

We extend an optimal entanglement distillation of the triplet Greenberger—Horne—Zeilinger (GHZ) state via entanglement concentrating in the three-partite partially electron-spin-entangled systems. Two entanglement concentration protocols are similarly designed in detail with the post-selection in quantum-dot (QD) and micro-cavity coupled systems. The proposed protocol can be repeated several rounds to achieve an optimal success probability with an assistance of the ancillary QD, where only the single photon needs to pass through the micro-cavity for each round. It increases the total success probability of the distillation even if the implemented cavity is imperfect in practice during the whole process.

We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein—Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.

Recently, an experimentally feasible three-party quantum sealed-bid auction protocol based on EPR pairs [Z.Y. Wang, Commun. Theor. Phys. 54 (2010) 997] was proposed. However, this study points out Wang's protocol cannot resist some internal bidders' attacks, such as the Twice-CNOT attack, the collusion attack. A malicious bidder can launch the Twice-CNOT attack to obtain the other's bid, or the dishonest auctioneer may collude with one bidder and help him/her win the action by changing his/her bid. For preventing against these attacks, a simple solution by using the QKD-based message encryption and a post-confirmation mechanism by adopting the hash function are proposed.

We investigate the dynamics of pairwise quantum discord (QD) for a mixed three-qubit W-type state in three independent non-Markovian reservoirs at zero temperature, each of which is modeled by a leaky cavity with Lorentzian spectral density. The influence of the environment's amount of non-Markovianity, the detuning between the qubit frequency and the cavity centre frequency, and the purity of the initial state on the QD dynamics are analyzed in detail. It is found that in the non-Markovian regime the system-reservoir interactions induce QD revivals and oscillations no matter whether the detuning is zero or not. Moreover, QD can be preserved for a long time if the non-Markovian condition and the detuning condition are satisfied simultaneously.

We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner—Nordström spacetime. This is accomplished when noticing that in order to produce the tetrad that locally and covariantly diagonalizes the stress-energy tensor, both the Monopole and the Coulomb fields are necessary in the construction. Without any of them it would be impossible to express the tetrad vectors that locally and covariantly diagonalize the stress-energy tensor. Then, both electromagnetic fields are an integral part of the same structure, the Reissner—Nordström geometry.

Considering the coupled nonlinear Schrödinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations. Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.

In this paper, we investigate a Josephson-junction device with dichotomous resistance or a special SQUID (superconducting quantum interference device). It is shown that frequency (stochastic) resonance and stochastic resonance can appear for some suitably selected parameters' values of the device respectively. Our results can provide some insights for the investigation of the SQUID response to the signal (including the input alternating current, the added alternating voltage, the vertically added alternating magnetic field, and the detected (electric-magnetic) temporal-periodic signal).

We derive the basic canonical brackets amongst the creation and annihilation operators for a two (1 + 1)-dimensional (2D) gauge held theoretic model of an interacting Hodge theory where a U(1) gauge field (A_μ) is coupled with the fermionic Dirac fields (ψ and ). In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries (and the concept of their generators) that are present in the theory. We do not use the definition of the canonical conjugate momenta (corresponding to the basic fields of the theory) anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries (and corresponding generators) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.

Among the Z-pole observables, A_FB^(0,b) and A_e display moderately large standard deviations from the Standard Model predictions. This result can be interpreted as independent experimental evidence for new physics beyond the SM, even if the 125 GeV Higgs-like boson at the LHC is ultimately confirmed as the SM Higgs. A recalculated global electroweak fit with a model-independent Z' shows that Z' can simultaneously suppress A_FB^(0,b) and A_e at the Z-pole, and reduce the largest deviation from 2.6σ in SM to 1.0σ in our scenario. The Z' fitting results also support a negative S parameter.

Pulse dynamics and stability in optical fibers in the presence of both self-steepening and quintic nonlinear effects are analyzed. Propagating profiles of the quintic derivative nonlinear Schrödinger model are isolated via two invariants of motion. The resulting canonical equation admits exact periodic propagating patterns in terms of the Jacobi elliptic functions, and solitary pulses are recovered in the long wave limit, i.e. degenerate cases of periodic profiles where each pulse is widely separated from the adjacent ones. Two families of such exact wave profiles are identified. The first one has a precise constraint concerning the magnitude of self-steepening and quintic nonlinear effects, while the second one permits more freedom. The reduction to the well established temporal soliton in an optical fiber waveguide in the absence of self-steepening and quintic nonlinearity is demonstrated explicitly. Numerical simulations are performed to identify regimes of parameter values where robust propagation patterns exist.

The Camassa-Holm equation, Degasperis—Procesi equation and Novikov equation are the three typical integrable evolution equations admitting peaked solitons. In this paper, a generalized Novikov equation with cubic and quadratic nonlinearities is studied, which is regarded as a generalization of these three well-known studied equations. It is shown that this equation admits single peaked traveling wave solutions, periodic peaked traveling wave solutions, and multi-peaked traveling wave solutions.

By investigating the diffraction of plane waves by a semi-infinite graphene layer, we present a rigorous solution for propagating surface plasmons in graphene, which can be excited by incident plane waves through the graphene edge. The theoretical results are confirmed by numerical simulations. Our results reveal a convenient way to excite propagating surface plasmons in graphene where the graphene edge plays an important role.

Recent experiments revealed the unusual strong spin effects with high spin selective transmission of electrons in double-stranded DNA. We propose a new mechanism that the strong spin effects could be understood in terms of the combination of the chiral structure, spin-orbit coupling, and especially spin-dependent Anderson localization. The presence of chiral structure and spin-orbit coupling of DNA induce weak Fermi energy splitting between two spin polarization states. The intrinsic Anderson localization in generic DNA molecules may result in remarkable enhancement of the spin selective transport. In particular, these two spin states with energy splitting have different localization lengths. Spin up/down channel may have shorter/longer localization length so that relatively less/more spin up/down electrons may tunnel through the system. In addition, the strong length dependence of spin selectivity observed in experiments can be naturally understood. Anderson localization enhanced spin selectivity effect may provide a deeper understanding of spin-selective processes in molecular spintronics and biological systems.

Bipartite entanglement, entanglement spectrum, and Schmidt gap in S=1 bond-alternative antiferromagnetic Heisenberg chain are investigated by the infinite time-evolving block decimation (iTEBD) method. The quantum phase transition (QPT) from the singlet-dimer phase to the Haldane phase can be detected by the singular behavior of bipartite entanglement, the sudden change of the entanglement spectrum, and the completely vanishing of the Schmidt gap. The critical point is determined to be around r_c ≃ 0.587, and the second-order character of the QPT is verified. Doubly degenerate entanglement spectra of both even and odd bonds are observed in the Haldane phase, by which one can distinguish the Haldane phase from the singlet-dimer phase easily. Nearest-neighbor antiferromagnetic correlations and next-nearest-neighbor ferromagnetic correlations are found in the whole parameter region. At the critical massless point, although exponentially decaying antiferromagnetic correlation is observed, it approaches to a constant value finally. Therefore, long-range correlations exist and the correlation length becomes divergent at the critical point.

An investigation of the optical properties of a GaAs spherical quantum dot which is located at the center of a Ga_1−xAl_xAs cylindrical nano-wire has been performed in the presence of an external electric held. The band nonparabolicity effect is also considered using the energy dependent effective mass approximation. The energy eigenvalues and corresponding wave functions are calculated by finite difference approximation and the reliability of calculated wave functions is checked by computing orthogonality. Using computed energy eigenvalues and wave functions, the linear, third-order nonlinear and total optical absorption coefficients and refractive index changes are examined in detail. It is found that (i) Presence of electric field causes both blue and red shifts in absorption spectrum; (ii) The absorption coefficients shift toward lower energies by taking into account the conduction band nonparabolicity; (iii) For large values of electric field the effect of conduction band nonparabolicity is less dominant and parabolic band is estimated correctly; (iv) In the presence of electric field and conduction band nonparabolicity the nonlinear term of absorption coefficient rapidly increases by increasing incident optical intensity. In other words, the saturation in optical spectrum occurs at lower incident optical intensities.

In this paper we consider quintessence reconstruction of interacting holographic dark energy in a non-flat background. As system's IR cutoff we choose the radius of the event horizon measured on the sphere of the horizon, defined as L = ar(t). To this end we construct a quintessence model by a real, single scalar field. Evolution of the potential, V(φ), as well as the dynamics of the scalar field, φ, is obtained according to the respective holographic dark energy. The reconstructed potentials show a cosmological constant behavior for the present time. We constrain the model parameters in a flat universe by using the observational data, and applying the Monte Carlo Markov chain simulation. We obtain the best fit values of the holographic dark energy model and the interacting parameters as c = 1.0576^{+0.3010+0.3052}_{−0.6632−0.6632} and ζ = 0.2433^{+0.6373+0.6373}_{−0.2251−0.2251}, respectively. From the data fitting results we also find that the model can cross the phantom line in the present universe where the best fit value of the dark energy equation of state is w_D = −1.2429.

We present Finslerian perturbation for the λCDM model, which breaks the isotropic symmetry of the universe. The analysis on the Killing vectors shows that the Randers—Finsler spacetime breaks the isotropic symmetry even if the scalar perturbations of the FRW metric vanish. In Randers—Finsler spacetime, the modified geodesic equation deduces a modified Boltzmann equation. We propose a perturbational version of the gravitational field equation in Randers—Finsler spacetime, where we have omitted the curvature tensor that does not belong to the base space of the tangent bundle. The gravitational field equations for the gravitational wave are also presented. The primordial power spectrum of the gravitational wave is investigated. We show that the primordial power spectrum for super-horizon perturbations is unchanged. For sub-horizon perturbations, however, the power spectrum is modified.