Table of contents

We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.

The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is proposed to localize a source density from loss-less wave-held measurements. Further, in order to recover source densities in a lossy medium, we first build attenuation operators thereby relating loss-less waves with lossy ones. Then based on asymptotic expansions of attenuation operators with respect to attenuation parameter, we propose two time reversal strategies for localization. The losses in electromagnetic wave propagation are incorporated using the Debye's complex permittivity, which is well-adopted for low frequencies (radio and microwave) associated with polarization in dielectrics.

A one-dimensional harmonic oscillator with position-dependent effective mass is studied. We quantize the oscillator to obtain a quantum Hamiltonian, which is manifestly Hermitian in configuration space, and the exact solutions to the corresponding Schrödinger equation are obtained analytically in terms of modified Hermite polynomials. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the position dependence of the mass vanishes.

We study the Bell-nonlocality dynamics of three remote atoms, two of which are trapped in one single-mode cavity and the third atom is trapped in another remote single-mode cavity. The interactions between the atoms and the cavity modes are studied via Tavis Cummings and Jaynes Cummings models. Here, the two single-mode cavities are introduced to simulate two different enviroments of the three atoms. The tripartite nonlocal correlations are studied in terms of the Svetlichny inequality and the WWZB inequality, respectively. The results show that the tripartite Bell-nonlocality sudden death will occur for the W state and GHZ state initial conditions. The detailed results demonstrate that the tripartite nonlocality of GHZ state is more robust than that of W state when suffering from the effect of environments.

We theoretically explore the possibility of observing the quantum decoherence of neutrino oscillation due to the vacuum dispersion, that the wave-packet of neutrino spatially splits according to the different velocities of two mass eigenstates. We find that if this decoherence could be observed and the range of values of the mixing angle is known, then the superluminal neutrino phenomena could occur for some mixing angles as the consequence of a weak measurement about flavor mixing in the neutrino propagation. Our calculation gives the explicit dependence of group velocity shift to the decoherence factor and the weak value of neutrino's pre and post-selected states. We also study the related problems for the neutrino oscillation with three generations.

Nonlocality, as an essential, subtle and intriguing aspect of nature, has many different facets and manifestations. In quantum information theory, nonlocality is usually defined, characterized and quantified in the framework of entanglement and violation of certain Bell inequalities. An exciting phenomenon concerning entanglement-related nonlocality is the superactivation, symbolized as "0 + 0 > 0", which means that two systems, while do not possess nonlocality individually by themselves, may exhibit nonlocality when combined together in an independent fashion. In this work, we explore nonlocality from the measurement perspective and reveal the superactivation of measurement-induced nonlocality (MIN): When two bipartite states with vanishing MIN are combined together, the tensorizing state may possess non-zero MIN. Implications and applications are discussed.

We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new bound on the minimum-error probability for ambiguous discrimination between arbitrary m quantum operations. This formulation consists only of Kraus-operators, the dimension, and the priori probabilities of the discriminated quantum operations, and is independent of input states. To some extent, we further generalize the bounds on the minimum-error probability for discriminating mixed states to quantum operations.

Based on the generalized uncertainty principle (GUP), we investigate the correction of quantum gravity to Hawking radiation of black hole by utilizing the tunnelling method. The result tells us that the quantum gravity correction retards the evaporation of black hole. Using the corrected covariant Dirac equation in curved spacetime, we study the tunnelling process of fermions in Schwarzschild spacetime and obtain the corrected Hawking temperature. It turns out that the correction depends not only on the mass of black hole but also on the mass of emitted fermions. In our calculation, the quantum gravity correction slows down the increase of Hawking temperature during the radiation explicitly. This correction leads to the remnants of black hole and avoids the evaporation singularity.

We perform the precision calculations for the e⁺e⁻ → q₋₋(q₋₋ = u₋ū₋, c₋₋,d₋₋, s₋₋) processes up to the QCD next-to-leading order (NLO) including full weak decays for the final T-odd mirror quarks in the littlest Higgs model with T-parity (LHT) at the Compact Linear Collider (CLIC). We show the dependence of the leading order (LO) and NLO QCD corrected cross sections on the colliding energy √s, and provide the LO and QCD NLO kinematic distributions of final particles. The results show that the LO cross section can be enhanced by the NLO QCD correction and the K-factor increases obviously when the threshold of the on-shell q₋₋-pair production approaches the colliding energy √s. The K-factor value varies in the range of 1.04 ∼ 1.41 in our chosen parameter space. We find that a simple approximation of multiplying the LO kinematic distribution with the integrated K-factor is not appropriate for precision study of the e⁺e⁻ → q₋₋(q₋₋ = u₋ū₋, c₋₋, d₋₋, s₋₋) processes, since the NLO QCD corrections are phase space dependent. It is necessary to calculate the differential cross sections including full NLO QCD corrections to get reliable results.

The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic held is studied in this paper. We map the noncommutative plane to a commutative one by means of Bopp shift and study this problem on the commutative plane. We find that this model can be mapped onto a quantum optics model which contains Anti—Jaynes—Cummings (AJC) or Jaynes—Cummings (JC) interactions when a dimensionless parameter ζ (which is the function of the intensity of the magnetic held) takes values in different regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ζ approaches the critical point. Several evidences of the chirality quantum phase transition are presented. We also study the non-relativistic limit of this model and find that a similar chirality quantum phase transition takes place in its non-relativistic limit.

The nuclear structure of ¹⁶O is studied in the framework of the particle-hole random phase approximation (ph RPA). The Hamiltonian is diagonalized within a model space with particle orbits {1d_5/2,1d_3/2, and 2s_1/2} and the hole orbits {1p_3/2 and 1p_1/2} using Warburton and Brown interaction WBP. The ph RPA calculations are tested, by comparing the electron scattering form factors with the available experimental data. The results of electron scattering form factors and reduced transition strength for the states: 1⁻, T = 0 (7.116 MeV); 2⁻, T = 1 (12.968 MeV); 2⁻, T = 1 (20.412 MeV); and 3⁻, T = 0 (6.129 MeV) are interpreted in terms of the harmonic-oscillator (HO) wave functions of size parameter b. The occupation probabilities of the single particle and hole orbits are calculated. The spurious states are removed by adding the center of mass (CM) correction to the nuclear Hamiltonian. A comparison with the available experiments data is presented.

The positive parity states in even-even ^152–166Dy are studied systematically in the framework of the interacting boson model (IBM). A cubic term, L = 3, has been added to the Hamiltonian in order to produce the effect of triaxiality on the energy spectrum. The potential energy surfaces as a function of β and γ deformation parameters, for all isotopes have been produced. Energy levels and reduced electric quadrupole transition probabilities are calculated in framework of IBM with Cubic term (IBMC). All results are compared with available experimental data. It is found that these isotopes can be described by a schematic Hamiltonian in transition from U(5) (vibration) to SU(3) (rotation) dynamic symmetry.

We study the stability properties of magnetized strange quark matter and strangelets under a strong magnetic field in the MIT bag model. The free energy per baryon of strange quark matter feels a great influence from the magnetic held. At the held strength about 10¹⁷ G, the magnetized strange quark matter becomes more stable. Considering the finite size effect, the magnetic influence on strangelets becomes complicated. For a given magnetic held, there exists a critical baryon number, below which the magnetized strangelets have lower energy than the non-magnetized strangelets. For the held strength of 5 × 10¹⁷ G, the critical baryon number is A_c ∼ 100. Generally, the critical baryon number increases with the decreasing external magnetic held. When the held strength is smaller than 10¹⁷ G, the critical baryon number goes up to A_c ∼ 10⁵. The stable radius, electric charge, and quark flavor fractions of magnetized strangelets are shown.

The behavior of the Goos—Hänchen (GH) shifts of the reflected and transmitted probe light beams is theoretically investigated. In a fixed geometrical configuration, the effect of quantum interference induced by spontaneous emission on the phase control of the GH shifts is analyzed in this paper. It is found that in a four-level N-type atomic system as an intracavity medium, the GH shifts of the reflected and transmitted probe light beam are completely phase dependent.

For studying the vortex structure in uniform dense dusty astrophysical conditions, a two-dimensional nonlinear equation is derived employing the quantum magnetoplasma hydrodynamic model and considering the strong collisional effect. The coherent vortex solution is obtained by perturbation analysis method. It is shown that the distribution of the electrostatic potential forms spatially a periodic vortex street, and is controlled temporally by the arbitrary function of time that may lead to abundant spacial distributions. It is found that the dust charge number, collision frequency, electron Fermi wavelength and quantum correction all play significant roles to the spatial distribution of vortex street.

We study the nonlinear propagation of dust-ion acoustic (DIA) shock waves in an un-magnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev—Petviashivili—Burgers (K-P-Burgers) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the K-P-Burgers equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.

The effects of plasma environments on energies, oscillator strengths, polarizabilities and hyperpolarizabilities for lithium atom have been calculated by combining the 1-dependent model potential of free lithium atom and linear variation method based on B-spline basis functions. The influence of plasma on lithium atom is represented by the Debye screened potential, which describes effectively the averaged effect of the plasma environment on atomic spectra. The results are in agreement with other reported ones.

A nonlinear propagation of cylindrical and spherical modified ion-acoustic (mIA) waves in an unmagnetized, collisionless, relativistic, degenerate multi-species plasma has been investigated theoretically. This plasma system is assumed to contain non-relativistic degenerate light ions, both non-relativistic and ultra-relativistic degenerate electron and positron fluids, and arbitrarily charged static heavy ions. The restoring force is provided by the degenerate pressures of the electrons and positrons, whereas the inertia is provided by the mass of ions. The arbitrarily charged static heavy ions participate only in maintaining the quasi-neutrality condition at equilibrium. The modified Burgers (mB) equation is derived by using reductive perturbation technique and numerically analyzed to identify the basic features of mIA shock structures. The basic characteristics of mIA shock waves are found to be significantly modified by the effects of degenerate pressures of electron, positron, and ion fluids, their number densities, and various charge state of heavy ions. The implications of our results to dense plasmas in astrophysical compact objects (e.g., non-rotating white dwarfs, neutron stars, etc.) are briefly discussed.

The first principles calculations based on density functional theory (DFT) are employed to investigate the mechanical properties and electronic structure of N and Ta doped TiC. The result shows that the co-doping of nitrogen and tantalum dilates the lattice constant and improves the stability of TiC. Nitrogen and tantalum can signiβcantly enhance the elastic constants and elastic moduli of TiC. The results of B/G and C₁₂–C₄₄ indicate tantalum can markedly increase the ductility of TiC. The electronic structure is calculated to describe the bonding characteristic, which revealed the strong hybridization between C-p and Ta-d and between N-p and Ti-d. The hardnessis is estimated by a semi-empirical model that is based on the Mulliken overlap population and bond length. While the weakest bond takes determinative role of the hardness of materials, the addition of Ta sharply reduces the hardness of TiC.

We present a comparative study of electronic structure and magnetic properties of Gd₅Si₄ and Gd₅Ge₄ compounds using first principles full potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT) using the WIEN2k code. The local-spin density approximation with correlation energy (LSDA+U) method has been used as the exchange-correlation potential. The optimized lattice constants are in good agreement with the experimental data. The total and partial density of states (DOS) of Gd₅Si₄ and Gd₅Ge₄ show the difference in Si 3p-Gd 5d and Ge 4p-Gd 5d hybridization, which have an effective role in indirect exchange interaction. In addition, the magnetic moments of Gd, Si, and Ge atoms and the compounds are calculated to clarify the differences in the magnetic properties of these compounds.

We investigate the quantum phase transition (QPT) and magnetocaloric effect (MCE) of a tetrameric chain with three-spin interaction using Green's function theory. The magnetization and gap analysis reveals a variety of quantum phases tuned by magnetic held and three-spin interaction, which can open up an energy gap, giving rise to the occurrence of zero magnetization plateau. However, strong three-spin couplings causing strong frustration will destroy the intermediate 1/2 plateau with emergence of a new gapless phase between two cusps. It favors achieving an enhanced MCE at the critical fields, where the minima of isoentropes as well as the valley-peak structure of Grüneisen ratio, signaling the accumulation of entropy, lead to cooling via adiabatic (de)magnetization processes. It is also found that the temperature dependence of specific heat combined with Grüneisen ratio can testify various quantum phases explicitly.

Heterogeneity of the neurons and noise are inevitable in the real neuronal network. In this paper, Gaussian white noise induced spatial patterns including spiral waves and multiple spatial coherence resonances are studied in a network composed of Morris—Lecar neurons with heterogeneity characterized by parameter diversity. The relationship between the resonances and the transitions between ordered spiral waves and disordered spatial patterns are achieved. When parameter diversity is introduced, the maxima of multiple resonances increases first, and then decreases as diversity strength increases, which implies that the coherence degrees induced by noise are enhanced at an intermediate diversity strength. The synchronization degree of spatial patterns including ordered spiral waves and disordered patterns is identified to be a very low level. The results suggest that the nervous system can profit from both heterogeneity and noise, and the multiple spatial coherence resonances are achieved via the emergency of spiral waves instead of synchronization patterns.

It has been found that, for the Supernova Legacy Survey three-year (SNLS3) data, there is strong evidence for the redshift-evolution of color-luminosity parameter β. In previous studies, only dark energy (DE) models are used to explore the effects of a time-varying β on parameter estimation. In this paper, we extend the discussions to the case of modified gravity (MG), by considering Dvali—Gabadadze—Porrati (DGP) model, power-law type f(T) model and exponential type f(T) model. In addition to the SNLS3 data, we also use the latest Planck distance priors data, the galaxy clustering (GC) data extracted from Sloan Digital Sky Survey (SDSS) data release 7 (DR7) and Baryon Oscillation Spectroscopic Survey (BOSS), as well as the direct measurement of Hubble constant H₀ from the Hubble Space Telescope (HST) observation. We find that, for both cases of using the supernova (SN) data alone and using the combination of all data, adding a parameter of β can reduce χ² by ∼ 36 for all the MG models, showing that a constant β is ruled out at 6σ confidence level (CL). Moreover, we find that a time-varying β always yields a larger fractional matter density Ω_m0 and a smaller reduced Hubble constant h; in addition, it significantly changes the shapes of 1σ and 2σ confidence regions of various MG models, and thus corrects systematic bias for the parameter estimation. These conclusions are consistent with the results of DE models, showing that β's evolution is completely independent of the cosmological models in the background. Therefore, our work highlights the importance of considering the evolution of β in the cosmology-fits.