The generalized nonlinear Schrödinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth solitary wave,kink and anti-kink wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given.Also,all possible explicit exact parametric representations of the waves are presented.

In this letter,the Lie point symmetries of the time fractional Fisher(TFF) equation have been derived using a systematic investigation.Using the obtained Lie point symmetries,TFF equation has been transformed into a different nonlinear fractional ordinary differential equations with the Erdélyi-Kober fractional derivative which depends on the parameter α.After that some invariant solutions of underlying equation are reported.

We study the Bell's inequality and multipartite entanglement generation for initially maximally entangled states of free Dirac field in a non inertial frame and asymptotically flat Robertson-Walker space-time.For two qubit case,we show that the Bell's inequality always is violated as measured by the accelerated observers which are in the causally connected regions.On the other hand,for those observers in the causally disconnected regions inequality is not violated for any values of acceleration.The generated three qubit state from two qubit state due to acceleration of one parties has a zero 3-tangle.For a three qubit state,the inequality violated for measurements done by both causally connected and disconnected observers.Initially GHZ state with non zero 3-tangle,in accelerated frame,transformed to a four qubit state with vanishing 4-tangle value.On the other hand,for a W-state with zero 3-tangle,in non inertial frame,transformed to a four qubit state with a non-zero 4-tangle acceleration dependent.In an expanding space-time with asymptotically flat regions,for an initially maximally entangled state,the maximum value of violation of Bell's inequality in the far past decreased in the far future due to cosmological particle creation.For some initially maximally entangled states,the generated four qubit state due to expansion of space-time,has non vanishing 4-tangle.

We consider a composite system:an anisotropic two-qubit Heisenberg XYZ chain coupled independently to their own environments.We take one of the qubit as the subsystem and the other qubit as an auxiliary qubit,and then the subsystem we concern can be considered to be coupled to a structured bath(auxiliary qubit+environments).Based on this,we study the non-Markovianity of the subsystem dynamics and show how the subsystem dynamics can be changed by manipulating the intensity of the qubit-qubit couplings or the anisotropy parameter.Moreover,we show how entanglement between the subsystem and the structured bath can be affected by the properties of the structured bath and the magnetic field.

The heat capacity and the electric capacitance of the black p-branes(BPB) are generally defined,then they are calculated for some special processes.It is found that the Ruppeiner thermodynamic geometry of BPB is flat.Finally,we give some discussions for the flatness of the Ruppeiner thermodynamic geometry of BPB and some black holes.

In this paper,we study lag synchronization between two coupled networks and apply two types of control schemes,including the open-plus-closed-loop(OPCL) and adaptive controls.We then design the corresponding control algorithms according to the OPCL and adaptive feedback schemes.With the designed controllers,we obtain two theorems on the lag synchronization based on Lyapunov stability theory and Barbalat's lemma.Finally we provide numerical examples to show the effectiveness of the obtained controllers and see that the adaptive control is stronger than the OPCL control when realizing the lag synchronization between two coupled networks with different coupling structures.

Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G'/G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.

CP violation effects of the Higgs stem from not only the CP mixing state but also the CP-violation couplings to electroweak bosons.The two CPV sources are combinedly studied based on an effective Higgs Lagrangian.The constraints from unitarity limits for WW and ZZ scatterings are investigated.We classify free parameters into five cases to analyze CP properties of the Boson.The allowed ranges are shown from fitting results to the signal strengths of the Higgs measured by ATLAS and CMS.

In this work we study the interaction of the coupled channels Ω_η and Ξ^* K within the chiral unitary approach.The systems under consideration have total isospins 0,strangeness S=-3,and spin 3/2.We study the s wave interaction which implies that the possible resonances generated in the system can have spin-parity J^P=3/2^-.The unitary amplitudes in coupled channels develop poles that can be associated with some known baryonic resonances.We find there is a dynamically generated 3/2^- Ω state with mass around 1800 MeV,which is in agreement with the predictions of the five-quark model.

In this paper we investigate the optical properties of an open four-level tripod atomic system driven by an elliptically polarized probe field in the presence of the external magnetic field and compare its properties with the corresponding closed system.Our result reveals that absorption,dispersion and group velocity of probe field can be manipulated by adjusting the phase difference between the two circularly polarized components of a single coherent field,magnetic field and cavity parameters i.e.the atomic exit rate from cavity and atomic injection rates.We show that the system can exhibit multiple electromagnetically induced transparency windows in the presence of the external magnetic field.The numerical result shows that the probe field in the open system can be amplified by appropriate choice of cavity parameters,while in the closed system with introduce appropriate phase difference between fields the probe field can be enhanced.Also it is shown that the group velocity of light pulse can be controlled by external magnetic field,relative phase of applied fields and cavity parameters.By changing the parameters the group velocity of light pulse changes from subluminal to superluminal light propagation and vice versa.

The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant walls.Mathematical modeling is based upon the laws of mass and linear momentum.Analytic solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number approximations.The features of the flow characteristics are analyzed by plotting the graphs of various values of physical parameters of interest.Trapping bolus scheme is also presented through streamlines.

We examine the effect of the electron exchange-correlation on weak and arbitrary amplitude quantum dust ion-acoustic(QDIA) solitons.The reduced quantum hydrodynamic(QHD) model is used.Carrying out a fully nonlinear analysis,it is found that the effect of the exchange-correlation on the main quantities for solitary-wave propagation can be quite important.In particular,it may be noted that the arbitrary amplitude QDIA soliton experiences a spreading as the phenomenon of exchange-correlation becomes effective.Furthermore,our results show that the exchange-correlation effects inhibit the formation of the flat-bottomed solitons and do not favor their emergence.It turns out that exchange-correlation and quantum diffraction may act concurrently to set up the conditions for the existence of the QDIA solitary waves.Our results complement and provide new insight into our previously published work on this problem.

In the present work,nonlinear interaction of elliptical laser beam with collisional plasma is studied by using paraxial ray approximation.Nonlinear differential equations for the beam width parameters of semi-major axis and semi-minor axis of elliptical laser beam have been set up and solved numerically to study the variation of beam width parameters with normalized distance of propagation.Effects of variation in absorption coefficient and plasma density on the beam width parameters are also analyzed.It is observed from the analysis that extent of self-focusing of beam increases with increase/decrease in plasma density/absorption coefficient.

Nonlinear structures of lower hybrid wave in collision plasmas are studied using the two-fluid theory.The oscillatory shock wave is observed due to the effects of the electron-neutral collision and the density inhomogeneity.In the cold electron limit,the oscillatory shock wave becomes the ordinary shock wave.In the collisionless limit,the dominated equation becomes KdV equation and the lower hybrid solitons arise.The amplitude of the nonlinear structure is depressed by the plasma inhomogeneity,but is hardly affected by the electron-neutral collision.

In this work,the influence of strain on threshold energy of absorption in Silicon circular nanowires is investigated.For this purpose,we first have used the density functional theory(DFT) to calculate the electron and hole effective masses.Then,we have obtained absorption threshold energy with two different procedures,DFT and effective mass approximation(EMA).We have also obtained the band structures of Si nanowires both DFT and EMA.The results show that:i) the expansive strain increases the hole effective mass while compressive strain increases the electron effective mass,ii) the electron and hole effective masses reduce with decreasing the wire size,iii) the absorption threshold energy decreases by increasing strain for compressive and tensile strain and its behavior as a function of strain is approximately parabolic,iv) the absorption threshold energy(for all sizes) obtained using EMA is greater than the DFT results.

Using the particle swarm optimization algorithm on crystal structure prediction,we first predict that MgY alloy undergoes a first-order phase transition from CsCl phase to P4/NMM phase at about 55 GPa with a small volume collapse of 2.63%.The dynamical stability of P4/NMM phase at 55 GPa is evaluated by the phonon spectrum calculation and the electronic structure is discussed.The elastic constants are calculated,after which the bulk moduli,shear moduli,Young's modui,and Debye temperature are derived.The brittleness/ductile behavior,and anisotropy of two phases under pressure are discussed in details.Our results show that external pressure can change the brittle behavior to ductile at 10 GPa for CsCl phase and improve the ductility of MgY alloy.As pressure increases,the elastic anisotropy in shear of CsCl phase decreases,while that of P4/NMM phase remains nearly constant.The elastic anisotropic constructions of the directional dependences of reciprocals of bulk modulus and Young's modulus are also calculated and discussed.

In this study,the structural and electronic properties of armchair graphdiyne nanoribbons,which have different widths are studied using the first principle calculation.The results indicate that all studied AGDYNRs show semiconducting behavior in which the band gap values decrease with the increase of nanoribbons width.The electronic and electrical properties of the graphdiyne sandwiched between two graphene nanoribbons are also investigated.The findings of our study indicate that among 4 investigated n-G-GDY-G-NR structures,the highest current is calculated for n=3(3-G-GDY-G-NR),due to phase transition.

We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrödinger equation.The accuracy of the solution is explored as it varies with the range of the numerical domain.The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires.Also,the model of a linear harmonic oscillator is considered for comparison reasons.It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range,which is thus considered to be optimal.This range is found to depend on the number of mesh nodes N approximately as α₀ log_e^α₁(α₂ N),where the values of the constants α₀,α₁,and α₂ are determined by fitting the numerical data.And the optimal range is found to be a weak function of the diffusion length.Moreover,it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrödinger equation.

We have investigated the dynamics of a protomer coupled to two different decoherent environments,each in a configuration called the spin star configuration.Using the quantum mechanics method,in different situations,we obtain the analytical expressions for the transition probability in the protomer system.In thermal equilibrium,there exist well-defined ranges of parameters for which decoherent interaction between the protomer and the environment assists energy transfer in the protomer system,while in pure quantum mechanics states,the decoherent interaction assists energy transfer for an eigenstate but against energy transfer for quantum mechanics averages.In particular,we also find that the dimerization of two bacteriochlorophylls in protomer can always assist energy transfer in certain parameter range,and in the appropriate spin bath energy,the efficiency of energy transport is sensitively depended on the temperature of environments.

A so-called ghost dark energy was recently proposed to explain the present acceleration of the universe.The energy density of ghost dark energy,which originates from Veneziano ghost of Quantum Chromodynamics(QCD),in a time dependent background,can be written in the form,ρ_D=(αH+βH²) where H is the Hubble parameter.We investigate the generalized ghost dark energy(GGDE) model in the setup of loop quantum Cosmology(LQC) and Galileon Cosmology.We study the cosmological implications of the models.We also obtain the equation of state and the deceleration parameters and differential equations governing the evolution of this dark energy model for LQC and Galileon Cosmology.

In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional KdV equation, the space-time fractional RLW equation, the space-time fractional Boussinesq equation, and the (3+1)-space- time fractional ZK equation. The solutions are expressed in terms of fractional hyperbolic and fractional trigonometric functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The analytical solution of homogenous linear FDEs with constant coefficients are obtained by using the series and the Mittag-Leffler function methods. The obtained results recover the well-know solutions when α= 1.

The Peregrine breather of order eleven (P₁₁ breather) solution to the focusing one-dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given: when all parameters are equal to 0 we recover the famous P₁₁ breather. We obtain new families of quasi-rational solutions to the NLS equation in terms of explicit quotients of polynomials of degree 132 in x and t by a product of an exponential depending on t. We study these solutions by giving patterns of their modulus in the (x; t) plane, in function of the different parameters.

Under condition of four potential fields, equations of motion and fluctuations in imaginary time are utilized to analytically derive the basic and fluctuating periodic instantons. It is shown that the basic instantons satisfy the elliptic or simple pendulum equations and their solutions are Jacobi elliptic functions, and fluctuating periodic instantons satisfy the Lamé equation and their solutions are Lamé functions. These results indicate that there exists the common solution family for different potential fields which are called the super-symmetry family.

A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition it also does not suffer from the recently raised critiques about quantum discord. The exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition. For bipartite mixed states the exact result can also be found for a special case. Furthermore the generalization into multipartite case is direct. It is shown that it can be evaluated exactly when the measured state is invariant under permutation or translation. In addition the detection of quantum phase transition is also discussed for Lipkin-Meshkov-Glick and Dicke model.

The conflict between the dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys. Rev. A 76 (2007) 052110], and has further been extended to a more general scenario [Phys. Rev. A 87 (2013) 052111]. In this paper, we reconsider Zurek's new derivation by using weak repeatability postulate or covariant condition instead of repeatability postulate.

The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential U =∑_i=1^d c_i|x_i/a_i|^n_i are studied carefully. Detailed calculation of Kim et al. (J. Phys. Condens. Matter 11 (1999) 10269) yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume C_V are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition in trapped systems as well.

In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann-Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada-Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed.

Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid (X.Z. Wang, Phys. Rev. E 66 (2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.

It has been found that a triple-node feed-forward motif has a function of signal amplification, where two input nodes receive the external weak signal and jointly modulate the response of the third output node [Liang et al., Phys. Rev. E 88 (2013) 012910]. We here show that the signal amplification can be further enhanced by adding a link between the two input nodes in the feed-forward motif. We further reveal that the coupling strength of the link regulates the enhancement of signal amplification in the modified feed-forward motif. We finally analyze the mechanism of signal amplification of such simple structure.

An alternative proof of factorization theorem for Drell-Yan process that works at operator level is presented in this paper. Contributions of interactions after the hard collision for such inclusive processes are proved to be canceled at operator level according to the unitarity of time evolution operator. After this cancellation, there are no longer leading pinch singular surface in Glauber region in the time evolution of electromagnetic currents. Effects of soft gluons are absorbed intoWilson lines of scalar-polarized gluons. Cancelation of soft gluons is attribute to unitarity of time evolution operator and such Wilson lines.

The operator level proof of factorization theorem exhibited in [arXiv:hep-ph/1307.4194] is extended to the semi-inclusive deep inelastic scattering process(SIDIS). Factorization theorem can be proved at operator level if there are not detected soft hadrons. The key point is that the initial one-nucleon state is the eigenstate of QCD.

The behaviors of barrier characteristics are analyzed for spherical-oblate systems over different configura- tions of colliding nuclei. For this purpose, we have extended our previous study [Phys. Rev. C 89 (2014) 054607], it is devoted to optimum “cold” and “hot” configuration] to analyze the same reaction systems in various configurations. The investigation on some chosen systems reveals that the barrier height and its position can be parameterized in times of the different orientations.

We propose the generation of photonic EPR state from quadratic waveguide array. Both the propagation constant and the nonlinearity in the array are designed to possess a periodical modulation along the propagation direction. This ensures that the photon pairs can be generated efficiently through the quasi-phase-matching spontaneous parametric down conversion by holding the spatial EPR entanglement in the fashion of correlated position and anticorrelated momentum. The Schmidt number which denotes the degree of EPR entanglement is calculated and it can approach a high value when the number of illuminated waveguide channels and the length of the waveguide array are properly chosen. These results suggest the quadratic waveguide array as a compact platform for engineering photonic quantum states in a high-dimensional Hilbert space.

In the present study, time evolution of quantum Cramer-Rao bound of entangled N00N state, as phase sensitivity, is determined by the aid of quantum estimation theory in the presence decoherence channels. Also, the dynamic quantum process as decoherence approach is characterized by quantum fisher information flow and entanglement amount in order to distinguish between Markovian and Non-Markovian process. The comparison between quantum fisher information and quantum fisher information flow assists to comprehend the phase sensitivity evolution corresponding to Non-Markovian and Markovian process. Furthermore, as result of backflow of information from the environment to system, the phase sensitivity corresponding memory effect of environment are revived after complete decay and increase in the few times.

Previous studies on modulation instabilities (MIs) in birefringent optical fibers focus on the ordinary linearly and circularly ones. This paper reports an analysis of MIs in the general elliptically birefringent fibers with the emphasis on investigating the effects of ellipticity angle (0°≤θ≤ 90°). Both symmetric and antisymmetric CW states are considered. In the anomalous dispersion regime, for the symmetric (antisymmetric) CW states, we show that MI gain increases dramatically (reduces first and then enhances greatly) as the increment of θ. In the normal dispersion regime, for the both CW states, the distinctive feature is that the gain of the MI bands reduces first, vanishes at θ= 45°, reappears across this ellipticity angle, and quickly increases after then.

The propagation and interaction between ion acoustic multi-solitons in an unmagnetized multicomponent plasma consisting of fluid hot ions, positrons and both hot and cold electrons, are investigated by employing the extended Poincare-Lighthill-Kuo (PLK) method. Two different Kortewege-de Vries (K-dV) equations are derived. The Hirota's method is applied to get the K-dV multi-solitons solution. The phase shift due to the overtaking and head- on collision of the multi-solitons is obtained.

The nonlinear propagation of dust acoustic waves is investigated in four-component plasmas consisting of positively charged dust grains, trapped ions, nonthermal electrons, and photoelectron due to ultraviolet irradiation. We use generalized viscoelastic hydrodynamic model for strongly coupled dust grain. In the weak nonlinearity limit, a modified Kadomstev-Petviashvili (KP) equation and a modified KP-Burger equation, which have a damping term coming from nonadiabatic charge variation, have been derived in the kinetic regime and hydrodynamic regime, respectively. With the increasing of UV photon flux, the hydrodynamic regime changes to kinetic regime. The approximate analytical line soliton and shock solutions are investigated in the kinetic regime and hydrodynamic regime, respectively.

We investigate bias and different barrier thicknesses effects on quantities related to spin and charge currents in MgO-based magnetic tunnel junctions. Using the non-Equilibrium Green's function formalism, we demonstrate that the in-plane and out-of-plane components of the spin-transfer torque have asymmetric and symmetric behaviors respectively. Magneto-resistance also decreases with increasing barrier thickness. The Landau-Lifshits-Gilbert equation describes the dynamics of the magnetization made by spin transfer torque. Increasing in spin current above its critical value or smaller the magnet reduces the switching time which is major result for making of new memory devices.

Based on the Wronskian technique and Lax pair, double Wronskian solution of the nonisospectral BKP equation is presented explicitly. The speed and dynamical influence of the one soliton are discussed. Soliton resonances of two soliton are shown by means of density distributions. Soliton properties are also investigated in the inhomogeneous media.

In this paper we have studied the dynamical evolution of Shannon information entropies in position and momentum spaces for two classes of (nonstationary) atom-field entangled states, which are obtained via the Jaynes-Cummings model and its generalization. We have focused on the interaction between two- and Ξ-type three-level atoms with the single-mode quantized field. The three-dimensional plots of entropy densities in position and momentum spaces are presented versus corresponding coordinates and time, numerically. It is observed that for particular values of the parameters of the systems, the entropy squeezing in position space occurs. Finally, we have shown that the well-known BBM (Beckner, Bialynicki-Birola and Mycielsky) inequality, which is a stronger statement of the Heisenberg uncertainty relation, is properly satisfied.