Table of contents

In this paper, the squared eigenfunction symmetries for the BTL and CTL hierarchies are explicitly constructed with the suitable modification of the ones for the TL hierarchy, by considering the BTL and CTL constraints. Also the connections with the corresponding additional symmetries are investigated: the squared eigenfunction symmetry generated by the wave function can be viewed as the generating function for the additional symmetries.

In this paper, we apply the source generation procedure to the coupled 2D Toda lattice equation (also called Pfaffianized 2D Toda lattice), then we get a more generalized system which is the coupled 2D Toda lattice with self-consistent sources (p-2D TodaESCS), and a pfaffian type solution of the new system is given. Consequently, by using the reduction of the pfaffian solution to the determinant form, this new system can not only be reduced to the 2D TodaESCS, but be reduced to the coupled 2D Toda lattice equation. This result indicates that the p-2D TodaESCS is also a pfaffian version of the 2D TodaESCS, which implies the commutativity between the source generation procedure and Pfaffianization is valid to the semi-discrete soliton equation.

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 examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.

In this paper we propose two quantum information splitting (QIS) schemes respectively for splitting an unknown single-qutrit and single-ququart state via three pairs of two-qubit partially entangled state. The necessary measurements and operations are given detailedly and the success probabilities are worked out. The two schemes can be directly generalized to QIS of multi-qutrit and multi-ququart states by using Bell-states channel.

We study the absorption probability and Hawking radiation of the scalar field in a d-dimensional black hole with quantum correction arising from the polymer quantization. We find that the quantum length scale k (i.e., the bounce radius) modifies the standard results in greybody factors and Hawking radiation on the brane and into the bulk. For the black hole with the larger mass M the effects of the parameter k in the four-dimensional black hole spacetime are entirely different from those in the high dimensional cases. When the mass of black hole M becomes very small, we also find that only the sign of the change rate of the greybody factors on the brane with respect to the dimensional number depends sharply on the bounce radius k. These information can help us know more about the extra dimension and the black holes with quantum correction.

We present a simple three-neuron Hopfield neural network as a tentative model to illustrate the perspective alternation of Necker cube. This neural network has a chaotic attractor with two "leaves", each leaf can be regarded as a dynamic process corresponding a feature of the Necker cube. This tentative model suggests another manifestation of the role of chaos in information processing.

The Carnot-like heat engines are classified into three types (normal-, sub- and, super-dissipative) according to relations between the minimum irreversible entropy production in the "isothermal" processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between η_C/2 and η_C/(2 − η_C), η_C/2 and η_C, 0 and η_C/(2 − η_C), respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Lett. 98 (2012) 40001] although the dissipative engines and the irreversible ones are inequivalent to each other.

The instanton induced cross section in deep inelastic kinematics is a subject which people are tendentious to investigate it. Instanton induced contributions are well defined for the nucleon structure function. The non-perturbative contribution to the quark distributions of structure function, F₂(x,Q²), is considered within an instanton model for the QCD vacuum. We find that the structure function may possess numerically large non-perterbative contributions which are related to the violation of chirality and correspond to the correction of parton distribution of the leading twist. It is shown that the instantons give a negative contribution to the structure function at the NLO approximation. A comparison between our results, considering instantaon effect, and the case when we do not take this effect is done. Taking into account the instanton size, ρ, via the modified running coupling constant we get to a good agreement between our results at the NLO and NNLO approximations and the available experimental data, specially at the low values of the Bjorken variable x < 0.1 which confirms the validity of our calculations.

Using the form factors calculated in the three-point QCD sum rules, we calculate the new physics contributions to the physical observables of B_c → D*_sμ⁺μ⁻ decay in a family non-universal Z' model. Under the consideration of three cases of the new physics parameters, we find that: (a) the Z' boson can provide large contributions to the differential decay rates; (b) the forward-backward asymmetry (FBA) can be increased by about 47%, 38%, and 110% at most in S1, S2, and extreme limit values (ELV), respectively. In addition, the zero crossing can be shifted in all the cases; (c) when > 0.08, the value of P_L can be changed from −1 in the Standard Model (SM) to −0.5 in S1, −0.6 in S2, and 0 in extreme limit values, respectively; (d) the new physics corrections to P_T will decrease the SM prediction about 25% for the cases of S1 and S2, 100% for the case of ELV.

In this paper, potential energy curves for the X¹Σ⁺, a³Π a'³Σ⁺, d³Δ, A¹Π and I¹Σ⁻ states of CO have been calculated using complete active space self-consistent field and multi-reference configuration interaction methods. The calculations have been performed at 108 nuclear separations from 0.7 to 4.0 Å by the aug-cc-PV5Z basis set. Spectroscopic constants for the six low-lying electronic states are found in good agreement with experimental data. The vibrational states of the X¹Σ⁺ and A¹Π states are also calculated, which are reliable and accurate by comparison with the experimental data and the other theoretical values. The transition dipole moment (TDM) shows that the TDM of the two states (X¹Σ⁺ → A¹Π) are reduced strongly with increase of bond length.

Optical bistability (OB) and optical multi-stability (OM) of a four-level Λ-type atomic system with two fold lower levels inside a unidirectional ring cavity is investigated. The effect of quantum interference arising from spontaneous emission and incoherent pumping on OB and OM is discussed. It is found that the threshold of OB and OM can be controlled by quantum interference mechanisms. In addition intensity of coupling field and the rate of an incoherent pumping field on behavior of OB and OM are then discussed.

Effects of ions charge-mass ratio on energy and energy spread of accelerated ions in laser driven plasma are investigated in detail by proposing a simple double-layer model for a foil target driven by an ultrastrong laser. The radiation pressure acceleration mechanism plays an important role on the studied problem. For the ions near the plasma mirror, i.e. electrons layer, the dependence of ions energy on their charge-mass ratio is derived theoretically. It is found that the larger the charge-mass ratio is, the higher the accelerated ions energy gets. For those ions far away from the layer, the dependence of energy and energy spread on ions charge-mass ratio are also obtained by numerical performance. It exhibits that, as ions charge-mass ratio increases, not only the accelerated ions energy but also the energy spread will become large.

The present article concerns the continuum modelling of the mechanical behaviour and equilibrium shapes of two types of nano-scale objects: fluid lipid bilayer membranes and carbon nanostructures. A unified continuum model is used to handle four different case studies. Two of them consist in representing in analytic form cylindrical and axisymmetric equilibrium configurations of single-wall carbon nanotubes and fluid lipid bilayer membranes subjected to uniform hydrostatic pressure. The third one is concerned with determination of possible shapes of junctions between a single-wall carbon nanotube and a fiat graphene sheet or another single-wall carbon nanotube. The last one deals with the mechanical behaviour of closed fluid lipid bilayer membranes (vesicles) adhering onto a fiat homogeneous rigid substrate subjected to micro-injection and uniform hydrostatic pressure.

Numerical simulations are employed to consider the problem of determining the granular temperatures of the species of a homogeneous heated granular mixture with a power-law size distribution. The partial granular temperature ratios are studied as functions of the fractal dimension D, the restitution coefficient e, the rescaled viscosity time, the average occupied area fraction φ, the total particle number N and the number fraction. Different species of particles in a power-law system typically do not have the same mean kinetic energy, namely the granular temperature. It is found that the extent of nonequipartition of kinetic energy is determined by the fractal dimension D, the restitution coefficient e and the rescaled viscosity time, while is insensitive to the total particle number N, the area fraction φ and the number fraction.

The development of spiral wave in a two-dimensional square array due to partial ion channel block (Potassium, Sodium) is investigated, the dynamics of the node is described by Hodgkin—Huxley neuron and these neurons are coupled with nearest neighbor connection. The parameter ratio x_Na (and x_K), which defines the ratio of working ion channel number of sodium (potassium) to the total ion channel number of sodium (and potassium), is used to measure the shift conductance induced by channel block. The distribution of statistical variable R in the two-parameter phase space (parameter ratio vs. poisoning area) is extensively calculated to mark the parameter region for transition of spiral wave induced by partial ion channel block, the area with smaller factors of synchronization R is associated the parameter region that spiral wave keeps alive and robust to the channel poisoning. Spiral wave keeps alive when the poisoned area (potassium or sodium) and degree of intoxication are small, distinct transition (death, several spiral waves coexist or multi-arm spiral wave emergence) occurs under moderate ratio x_Na (and x_K) when the size of blocked area exceeds certain thresholds. Breakup of spiral wave occurs and multi-arm of spiral waves are observed when the channel noise is considered.

We apply the statefinder diagnostic to the extended holographic Ricci dark energy (ERDE) model without and with interaction to study their behaviors. We plot the trajectories of various parameters for different cases. It is shown that the non-interacting model does not reach the LCDM point {1, 0} and the interacting one is favored, because the interaction makes the evolution of the statefinder pair {r, s} quite different.

We propose a new type of dark energy (DE) model, in which the equation of state of DE ω_de is a simple function of the fractional energy density Ω_de instead of the redshift z. We assume three DE models of this type, and fit them with present observations to get constraints of DE, which are also compared with the CPL model. It is shown that a suitable ω_de(Ω_de) model can give smaller χ² or smaller errors of ω_de than that of the CPL model. This new type of DE model can help to study the essential properties and nature of DE.