By using the bosonization and renormalization group methods, we have studied the low energy physical properties in one-dimensional extended Hubbard model. The formation of charge and spin gaps is investigated at the half-filled electron band. An analytical expression for the charge gap in terms of the Coulomb repulsive interaction strength U and the nearest-neighbour interaction parameter V is obtained.

In this paper we propose a novel and efficient quantum secret sharing protocol using d-level single particle, which it can realize a general access structure via the thought of concatenation. In addition, Our scheme includes all advantages of Tavakoli's scheme[Phys. Rev. A 92 (2015) 030302(R)]. In contrast to Tavakoli's scheme, the efficiency of our scheme is 1 for the same situation, and the access structure is more general and has advantages in practical significance. Furthermore, we also analyze the security of our scheme in the primary quantum attacks.

In this paper, we study the problem of sampling complexity for channel discrimination with respect to two different strategies: product strategy and adaptive strategy. We first formally introduce the definitions of the sampling complexity of the channels under the framework of hypothesis testing , wherein the goal is to determine the minimum number of samples needed to reach a desired error probability. We then establish the lower and upper bounds on the sampling complexity of the symmetric, asymmetric, and error exponent hypothesis testing settings. We show that, by imposing product strategy on testing, the bounds are always characterized by the generalized channel divergence, while with adaptive strategy, the bounds are characterized by the amortized channel divergence. Finally, we analyze two concrete examples, and obtain that the adaptive strategy can not lead to an advantage to the problem of determining the sampling complexity for classical-quantum channels, which can bring advantages for generalized amplitude damping channels.

Using relativistic spin-flavor wave functions of a Lorentz-covariant light cone quark model, we calculate the electromagnetic form factors of two S₁₁ resonances, N(1535) and N(1650), and the helicity amplitudes A_1/2 and S_1/2 for electroexcitation of the S₁₁ resonances from the nucleon. The electromagnetic form factors of these S₁₁ resonances are found to be similar to those of the nucleon in shape, while the charge form factor of neutral N(1650) is nearly zero. The relative peak height of the S₁₁ charge form factors is controlled by the mixing angle common to both resonance wave functions. As in most quark models, there is a systematic overestimate of A^p_1/2 in both N(1535) and N(1650) cases at the photon point. A sizeable S_1/2 for all cases is produced as suggested by experiments.

We have proposed a quantum system with equally-distant partially-entangled alphabet states which has the minimal mutual overlap and the highly distinguishability, these quantum states are used as the “signal states” of the quantum communication. We have also constructed the positive operator-valued measure for these “signal states” and discussed their entanglement properties and measurement of entanglement. We calculate the accessible information for these alphabet states and show that the accessible information is closely related to the entanglement of the “signal states”: the higher the entanglement of the “signal states”, the better the accessible information of the quantum system, and the accessible information reaches its maximal value when the alphabet states have their maximal entanglement.

In this paper, we consider a system of (2+1)-dimensional nonlinear models by using CK direct method and Hereman-Nuseir method generated by the Jaulent-Miodek Hierarchy. We construct some new multiple kink and singular kink solutions of (2+1)-Dimensional Nonlinear Models with the aid of symbolic computation.

We calculate the lowest-order quantum-interference correction to the density of states (DOS) of weakly-disordered two-dimensional (2D) tight-binding square lattices around half filling. The impurities are assumed to be randomly distributed on small fractions of the sites, and have a strong potential yielding a unitary-limit scattering. In addition to the usual diffusive modes in the retarded-advanced channel, there appear diffusive π modes in the retarded-retarded (or advanced-advanced) channel due to the existence of particle-hole symmetry. It is found that the π-mode diffuson gives rise to a logarithmic suppression to the DOS near the band center, which prevails over the positive correction contributed by π-mode cooperon. As a result, the DOS is subject to a negative total correction. This result is qualitatively different from the divergent behavior of the DOS at the band center predicted previously for disordered 2D two-sublattice models with the particle-hole symmetry.

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.

Unravelling the source of quantum computing power has been a major goal in the field of quantum information science. In recent years, the quantum resource theory (QRT) has been established to characterize various quantum resources, yet their roles in quantum computing tasks still require investigation. The so-called universal quantum computing model (UQCM), e.g. the circuit model, has been the main framework to guide the design of quantum algorithms, creation of real quantum computers etc. In this work, we combine the study of UQCM together with QRT. We find, on one hand, using QRT can provide a resource-theoretic characterization of a UQCM, the relation among models and inspire new ones, and on the other hand, using UQCM offers a framework to apply resources, study relation among these resources and classify them. We develop the theory of universal resources in the setting of UQCM, and find a rich spectrum of UQCMs and the corresponding universal resources. Depending on a hierarchical structure of resource theories, we find models can be classified into families. In this work, we study three natural families of UQCMs in detail: the amplitude family, the quasi-probability family, and the Hamiltonian family. They include some well known models, like the measurement-based model and adiabatic model, and also inspire new models such as the contextual model that we introduce. Each family contains at least a triplet of models, and such a succinct structure of families of UQCMs offers a unifying picture to investigate resources and design models. It also provides a rigorous framework to resolve puzzles, such as the role of entanglement versus interference, and unravel resource-theoretic features of quantum algorithms.

Charge-dependent correlations from both background and charge separation contribute to experimental observables in heavy-ion collisions. In this paper, we use stochastic hydrodynamics to study background charge asymmetry due to fluctuations. Using the rapidity-dependent correlation and a simple ansatz for particle distributions, we find a fluctuation-induced correlation to provide a type of background F -correlation. Experimental data for Au+Au collisions at $\sqrt{{s}_{\mathrm{NN}}}=200\,\mathrm{GeV}$ are compared. We also make predictions for F -correlations in isobar collisions. Combining this with our previous chiral magnetic effect results, we obtain δ -correlations for collisions in the three types of system. Computations from our model show an almost identical background with less than 2% difference for isobars, but roughly 10% difference for their charge separations. In combination with our earlier works, we provide a consistent method of calculating both the chiral magnetic effect and the charged background in the context of stochastic hydrodynamics.

The time evolution of an initially localized mode in a one-dimensional lattice with off-diagonal nonlinearity disorder is studied by solving a modified nonlinear Schrodinger equation. Absence of localization is found when the nonlinearity parameter is beyond the selftrapping region for corresponding periodic httice. The propagation of electrons shows ballistic behavior even in the presence of disorder. When self-trapping occurs, the untrapped portion still escapes ballistically.

The way of handling boundary conditions with simple bounce-back rule in the lattice gas and lattice Boltzmann method had been considered as one of the advantage compared with other numerical schemes. The half-way bounce-back rule inherits the advantage of the bounce-back rule and improves the accuracy to the second-order on flat boundaries. In this paper, we test the possible application of the half-way bounce-back rule to the system with complex geometry. Our simulation results show that the half-way bounce-back rule is a good boundary condition in the problems without emphasis on accuracy.

In this paper, based on the adjacency matrix of the network and its powers, the formulas are derived for the shortest path and the average path length, and an effective algorithm is presented. Furthermore, an example is provided to demonstrate the proposed method.

Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4,R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4,R)\supset U(2).

We present a simple, general method for calculating the binding energies of excitons in semiconductor quantum wires. The binding energy is given by an integral (over the electron and hole two-dimensional coordinates perpendicular to the wire) of a prescribed function weighted by the squares of the electron and hole subband envelope functions. Taking as an example, we calculate the binding energy of exciton in quantum wires assuming an infinite confining potential. This method should be applicable to a variety of more complex systems.

In this work, ionization potentials and quantum effects of 1s²np²P Rydberg states of lithium are calculated based on the calibrated quantum defect function. Energy levels and quantum defects for 1s²np²P bound states and their adjacent continuum states are calculated with the R-matrix theory, and then the quantum defect function of the 1s²np (n≥7) channel is obtained, which varies smoothly with the energy based on the quantum defect theory. The accurate quantum defect of the 1s²7p²P state derived from the experimental data is used to calibrate the original quantum defect function. The new function is used to calculate ionization potentials and quantum effects of 1s²np²P (n≥7) Rydberg states. Present calculations are in agreement with recent experimental data in whole.

The time evolution of the time-dependent harmonic oscillator is studied by a sequence of unitary transformations and the exact evolving state for the system is obtained. A specific model of frequency variation for the time-dependent harmonic oscillator is discussed as an illustrative example.

In this paper, the Adomian's decomposition method (ADM) is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.

We review the problem of dark energy, including a survey of theoretical models and some aspects of numerical studies.

The solutions of the Laplace equation in n-dimensional space are studied. The angular eigenfunctions have the form of associated Jacobi polynomials. The radial solution of the Helmholtz equation is derived.

We provide a new expression of the quantum Fisher information (QFI) for a general system. Utilizing this expression, the QFI for a non-full rank density matrix is only determined by its support. This expression can bring convenience for an infinite-dimensional density matrix with a finite support. Besides, a matrix representation of the QFI is also given.

Hamiltonian of a one-dimensional Bose-Hubbard model is re-formulated by using differential realization of the boson algebra. Energy matrices can then be generated systematically by using a Mathematica package. The output can be taken as the input of other diagonalization codes. As examples, exact energy eigenvalues and the corresponding wavefunctions for some cases are obtained with a Fortran diagonalization code. Phase transition of the model is analyzed.

We connect magic (non-stabilizer) states, symmetric informationally complete positive operator valued measures (SIC-POVMs), and mutually unbiased bases (MUBs) in the context of group frames, and study their interplay. Magic states are quantum resources in the stabilizer formalism of quantum computation. SIC-POVMs and MUBs are fundamental structures in quantum information theory with many applications in quantum foundations, quantum state tomography, and quantum cryptography, etc. In this work, we study group frames constructed from some prominent magic states, and further investigate their applications. Our method exploits the orbit of discrete Heisenberg–Weyl group acting on an initial fiducial state. We quantify the distance of the group frames from SIC-POVMs and MUBs, respectively. As a simple corollary, we reproduce a complete family of MUBs of any prime dimensional system by introducing the concept of MUB fiducial states, analogous to the well-known SIC-POVM fiducial states. We present an intuitive and direct construction of MUB fiducial states via quantum T-gates, and demonstrate that for the qubit system, there are twelve MUB fiducial states, which coincide with the H-type magic states. We compare MUB fiducial states and SIC-POVM fiducial states from the perspective of magic resource for stabilizer quantum computation. We further pose the challenging issue of identifying all MUB fiducial states in general dimensions.

In this paper, a classical system of ordinary differential equations is built
to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-imensional equations by using the generating function method. Besides the Birkhoffian structure-preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f. Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.

With the help of the effective refractive index method we have numerically analyzed a multilayer planar waveguide structure and calculated the propagation constants, confinement factors, and transverse electric (TE) modes. A five-layer waveguide model has been provided to analyze the electro-magnetic wave propagation process. The analysis method has been applied to the 980 nm laser with active layer of GaInAs/GaInAsP strained quantum wells, GaInAsP confinement layers and GaInP cap layers. By changing the thickness of confinement layers, we obtained confinement factor as high as 95% with higher TE modes TE1 and TE2. The results are in good agreement with the experiment by A. Al-Muhanna et al. and give the new idea to enhance output power of semiconductor lasers. The analysis method can also be extended to any other slab multilayer waveguide structures, and the results are useful to the fabrication of optic-electronic devices.

Surface properties of SiC power devices mostly depend on the passivation layer (PL).This layer has direct influence on electrical characteristics of devices.2D numerical simulation of forward and reverse characteristics with and without different (PLs) (SiO₂,HfO₂ and Si₃N₄) has been performed.Simulation results show that the breakdown voltage increases with increasing PL thickness,and there is a lesser significant effect on forward characteristics.The maximum breakdown voltage with and without SiO₂ PL is 1240 V and 276 V,respectively.SiO₂ PL has compatibility with SiC surface providing high breakdown voltage,6 and 8% higher than that of HfO₂ and Si₃N₄ respectively.Low leakage current is observed which then further decreases on reducing the thickness of PL.Furthermore,variation of forward current with dielectric constant and thickness of PLs was observed.Finally,it is suggested that matches of our results with published experimental results indicate that the Sentaurus TCAD simulator is a predictive tool for the SiC Schottky barrier diode simulation.

The linear-muffin-tin orbital method is used to study the electronic-energy-band structure of zinc-blende CdS. Incorporating the 4d states of Cd into the valence band gives substantially the main-valenceband width, and yields valenceband features in agreement with the experiment. The calculated equilibrium lattice constant is in accord with the measured result. The fundamental band gap is found to be direct at T point and the value is about 1.21 eV. The band structure calculation shows that the present results are in good agreement with experiments and other calculations.

The recurrence relations are presented for the calculation of basic overlap integrals, by making use of which other overlap integrals are calculated analytically. These recurrence relations are especially useful for the calculation of any overlap integral for large quantum numbers. For the arbitrary values of screening constants of atomic orbitals and internuclear distances an accuracy of the computer results is satisfactory for the values of principal quantum numbers of Slater functions up to 50.

A general solution of sun tracking for an arbitrarily oriented heliostat towards an arbitrarily located target on the earth is published. With the most general form of solar tracking formulae, it is seen that the used azimuth-elevation, spinning-elevation tracking formulae etc. are the special cases of it. The possibilities of utilizing the general solution and its significance in solar energy engineering are discussed.

The linear variable separation approach is successfully extended to (1+1)-dimensional Korteweg-de Vries (KdV) type models related to Schrödinger system. Some significant types of solitons such as compacton, peakon, and loop solutions with periodic behavior are simultaneously derived from the (1+1)-dimensional soliton system by entrancing appropriate piecewise smooth functions and multivalued functions.

It is pointed out that the assertion that the eigenfunction of the creation operator a⁺ is identically zero is not rigorous.On the contrary, the eigenfunction of a⁺ may be discussed by using the contour integral representation of δ function, the property of which and the relation with the eigenstate of the annihilation operator are discussed. Its applications, especially the application in thoroughly studying the inverse operator's properties, are presented. It is shown that the phase operator can also be represented by the inverse operator.

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states. we find a link to some entanglement measures through some new parameters (amplitudes of coherent states). Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of  Bell inequality for a class of mixed states with the degree of
entanglement by applying the formalism of Horodecki  et al.

An exact analogy is approached between systems in thermal equilibrium and those far from equilibrium which can be the cases without detailed balance. The analogy is based on the requirement that a given drift in the Fokker-Planck equation can be decomposed into two parts, one of which is divergence-free and the other can be derived from a potential which is invariant along the direction of the first part. If the conditions are fulfilled the Fokker-Planck equation changes in to a standard Poisson equation. The relations of this requirement to other conditions are diecussed. As a concrete example, the stationary Fokker-Planck equation for optical bistability is solved by using"this method.

The amorphous silicon nanoparticles (Si NPs) embedded in silicon nitride (SiN_x) films prepared by helicon wave plasma-enhanced chemical vapor deposition (HWP-CVD) technique are studied. From Raman scattering investigation, we determine that the deposited film has the structure of silicon nanocrystals embedded in silicon nitride (nc-Si/SiNx) thin film at a certain hydrogen dilution amount. The analysis of optical absorption spectra implies that the Si NPs is affected by quantum size effects and has the nature of an indirect-band-gap semiconductor. Further, considering the effects of the mean Si NP size and their dispersion on oscillator strength, and quantum-confinement, we obtain an analytical expression for the spectral absorbance of ensemble samples. Gaussian as well as lognormal size-distributions of the Si NPs are considered for optical absorption coefficient calculations. The influence of the particle
size-distribution on the optical absorption spectra was systematically studied. We present the fitting of the optical absorption experimental data with our model and discuss the results.

The lattice parameters, bulk modulus, phase transition pressure, and temperature dependencies of the elastic constants c_ij of CdSe are investigated by using the Cambridge Serial Total Energy Package (CASTEP) program in the frame of Density Functional Theory (DFT). It is found that the phase transitions from the ZB structure to the RS structure and from WZ structure to RS structure are 2.2 GPa and 2.8 GPa, respectively. Our results agree well with the available experimental data and other theoretical results. The aggregate elastic modulus (B, G, E, A), the Poisson's ratio (υ), the Grüneisen parameter (γ), the Debye temperature Θ_D on pressure and temperature are also successfully obtained.

Spin-wave expansion is used to evaluate the staggered magnetization of frustrated antiferromagnetic (AF) Heisenberg model with next-nearest-neighbor exchange couplings on a square lattice to the order O(1/S) at zero temperature. It is shown that the O(1/S) order correction increases the staggered magnetization and its presence invalidates the conventional spin- wave conclusions at large frustrations. We apply the mean-field approximation to deal with the quartic terms in the Hamiltonian of the Holstein-Primakoff transformation. A phaqe diagtam is obtained, suggesting that the NCel order is not destroyed for S≥1 at any frustration, while for S = 1/2 there may exist a disordered phase for strong frustrations.

The explicit forms of the quantum Clebsch-Gordan coefficients and the first-type quantum Racah coefficients for the quantum sl(2) enveloping algebra are computed in detail. Exact values of some coefficients are listed. An important relation, quantum Racah sum rule, is proved.

The notes here presented are of the modifications introduced in the application of WKB method. The problems of two- and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulation of quantization rule respectively. It is found that the energy spectrum of the radial harmonic oscillator, which is reproduced exactly by the standard WKB method with the Langer modification, is also reproduced exactly without the Langer modification via the new quantization rule approach. An alternative way to obtain the non-integral Maslov index for three-dimensional harmonic oscillator is proposed.

Simultaneously optimizing the estimation of the centroid and separation of two incoherent optical point sources is constrained by a tradeoff relation determined by an incompatibility coefficient. At the Rayleigh distance, the incompatibility coefficient vanishes and thus the tradeoff relation no longer restricts the simultaneous optimization of measurement for a joint estimation. We construct such a joint optimal measurement by an elaborated analysis on the operator algebra of the symmetric logarithmic derivative. Our work not only confirms the existence of a joint optimal measurement for this specific imaging model, but also gives a promising method to characterize the condition on measurement compatibility for general multiparameter estimation problems.