Table of contents

A new isospectral problem is firstly presented, then we derive integrable system of soliton hierarchy. Also we obtain new integrable couplings of the generalized Kaup—Newell soliton equations hierarchy and its Hamiltonian structures by using Tu scheme and the quadratic-form identity. The method can be generalized to other soliton hierarchy.

The hybrid lattice, known as a discrete Korteweg-de Vries (KdV) equation, is found to be a discrete modified Korteweg-de Vries (mKdV) equation in this paper. The coupled hybrid lattice, which is pointed to be a discrete coupled KdV system, is also found to be discrete form of a coupled mKdV systems. Delayed differential reduction system and pure difference systems are derived from the coupled hybrid system by means of the symmetry reduction approach. Cnoidal wave, positon and negaton solutions for the coupled hybrid system are proposed.

The double Wronskian solutions of the non-isospectral Levi equations are derived through Wronskian technique.

A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given.

In this paper, the two different Darboux transformations for a Blaszak—Marciniak (BM) three-field lattice equation are constructed. As the applications of the obtained Darboux transformations, new explicit solutions for the BM lattice are given. We also discuss some properties for these new explicit solutions. Our analysis shows that the explicit solutions possess new characters.

In this work, we consider an evolutionary prisoner's dilemma game on a homogeneous random network with the richest-following strategy adoption rule. By constructing homogeneous random networks from a regular ring graph, we investigate the effects of topological randomness on cooperation. In contrast to the ordinary view that the presence of small amount of shortcuts in ring graphs favors cooperation, we find the cooperation inhibition by weak topological randomness. The explanations on the observations are presented.

In this paper, we categorify the algebra U_q with the same approach as in [A. Lauda, Adv. Math. (2010), arXiv:math.QA/0803.3652; M. Khovanov, Comm. Algebra 11 (2001) 5033]. The algebra U̇ = U̇_q is obtained from U_q by adjoining a collection of orthogonal idempotents 1_λ, λ ∊ P, in which P is the weight lattice of U_q. Under such construction the algebra U is decomposed into a direct sum ⊕_λ∊P 1_λ'U1_λ. We set the collection of λ ∊ P as the objects of the category , 1-morphisms from λ to λ' are given by 1_λ'U 1_λ, and 2-morphisms are constructed by some semilinear form defined on U. Hence we get a 2-category from the algebra U_q.

The quantum phase transition in the isotropic XY chain with three-site interaction has been studied by calculating the quantum discord, classical correlation, and concurrence measuring entanglement. It is found that the quantum discord is a better choice than concurrence to signal the presence of the quantum phase transition in this model, since that for next-nearest neighbor spins the derivative of the quantum discord still exhibits singularity at the critical point while there is no more entanglement.

The effective mass one-dimensional Schrödinger equation for the generalized Morse potential is solved by using Nikiforov—Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.

The second reference state of the open XYZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz.

We investigate the thermal entanglement in the Lipkin—Meshkov—Glick (LMG) model which consists of spin-1/2 particles with XXZ-type exchange interactions between any pair of them. The ferromagnetic (FM) and antiferromagnetic (AFM) cases are completely analyzed at both finite temperature and zero temperature. According to the results obtained by accurate numerical calculation, several interesting physic phenomena and characteristics of thermal entanglement in the LMG model are found. Not only do we evaluate the entanglement of the LMG model, but also discover the correlations between macroscopic physical quantities and thermal entanglement.

Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.

Quantum Zeno effect with mixed initial state is studied here. Frequent projective measurements performed on a bipartite joint pure state system will result in the quantum Zeno effect on the subsystem of interest. This shows the existence of Quantum Zeno effect in the system with mixed initial states.

We study the influence of screening effect on quantum decoherence for charge qubit and the process of quantum information storage. When the flux produced by the circulating current in SQUID loop is considered, screening effect is formally characterized by a LC resonator. Using large-detuning condition and Fröhlich transformation in the qubit-cavity-resonator system, we calculate the decoherence factor for charge qubit and the effective qubit-cavity Hamiltonian. The decoherence factor owns a factorized structure, it shows that screening effect is a resource of decoherence for charge qubit. The effective Hamiltonian shows that the screening effect results in a frequency shift for charge qubit and a modified qubit-cavity coupling constant induced by a LC resonator.

A multiparty quantum secret sharing (MQSS) protocol with two-photon three-dimensional Bell states was proposed by Gao [Commun. Theor. Phys. 52 (2009) 421] recently. This study points out that the performance of Gao's protocol can be much improved by using the technique of decoy single photons and carefully modifying the protocol to remove some unnecessary unitary operations, devices, and transmissions.

The entanglement resonance in anisotropic spin-1/2 Heisenberg chains of different couplings is investigated when the nearest neighbor coupling is periodically modulated with external magnetic field. When the modulation frequency equals twice of the magnetic field, the entanglement resonance is larger than that at other modulation frequencies and decreases as the number of spins in the chain increases. When the modulation frequency equals the magnetic field, the entanglement resonance can be reduced to a quite low value by varying the coupling along z axis.

We give the brief review on the related definition of the geometric phase independent of specific physical system based on the displacement opreator and the sqeezed operator, then show how the displacement operator and the squeezed operator can induce the general geometric phase. By means of the displacement operator and the squeezed operator concerning the circuit cavity mode state along a closed path in the phase space, we discuss specifically how to implement a two-qubit geometric phase gate in circuit quantum electrodynamics with both single photon interaction and two-photon interaction between the superconducting qubits and the circuit cavity modes. The experimental feasibility is discussed in detail.

In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schrödinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of commutators, defining the time evolution in terms of a non-Hermitian Hamiltonian, onto a non-Hamiltonian algebra with a Hermitian Hamiltonian. The logic behind such a derivation is reversible, so that any Hermitian Hamiltonian can be used in the formulation of non-Hermitian dynamics through a suitable algebra of generalized (non-Hamiltonian) commutators. These results provide a general structure (a template) for non-Hermitian equations of motion to be used in the computer simulation of open quantum systems dynamics.

Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the theory to non-equilibrium domain, however the status of the theory of non-equilibrium phenomena can not be said so well established as the Gibbsian ensemble theory. In this work, we present a formalism for the non-equilibrium statistical ensemble based on a subdynamic kinetic equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.

In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator on the rational noncommutative orbifold T²/Z₄. we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.

At the CERN large hadron collider (LHC), production of the Higgs boson in association with Z or W bosons provides a dramatic experimental signal for detecting the standard model (SM) Higgs boson. In this paper, we consider the contributions of the left-right twin Higgs (LRTH) model to the processes q' → Z (W) H. Our numerical results show that, in the favorable parameter spaces, the cross sections deviate distinctly from the predictions of the SM. The possible signals of the LRTH model can be detected via these processes at the LHC experiments.

Based on the low energy effective Hamiltonian with naive factorization, we calculate the branching ratios (BRs) and CP asymmetries (CPAs) for the twenty three double charm decays B/B_s → D^(*)_(s)D^(*)_(s) in both the standard model (SM) and the minimal supergravity (mSUGRA) model. Within the considered parameter space, we find that (a) the theoretical predictions for the BRs, CPAs and the polarization fractions in the SM and the mSUGRA model are all consistent with the currently available data within ±2σ errors; (b) For all the considered decays, the supersymmetric contributions in the mSUGRA model are very small, less than 7% numerically. It may be difficult to observe so small SUSY contributions even at LHC.

We study the statistics of the emitted filed from Rydberg atom confined inside a microcavity and interacting with a pump laser in the strong coupling regime. We explore the manifestation of the antibunching in connection with the internal system parameters.

We study the dynamics of the entropy correlations and entanglement in a system of interaction of a superconducting charge qubit with a single-mode resonant cavity subject to noise considered as two-state random phase telegraph noise. We show that although the noise has an apparent suppressing effect on the evolution of the entropies of the qubit and the field and also on the entanglement in the system, the entropy exchange between the qubit and the field is independent of it during the time evolution of the system.

The problem of the mixed convection in a cubic cavity is studied with lattice Boltzmann method. A multiple-relaxation-time lattice Boltzmann model for incompressible flow in the cubic cavity and another thermal lattice Boltzmann model for solving energy/temperature equation are proposed. The present models are first validated through a comparison with some available results, and then, we present a detailed parameter study on the mixed convection in the cubic cavity. The numerical results show that the flow and temperature patterns change greatly with variations of the Reynolds and Richardson numbers.

Violations of Bell inequality, Cauchy—Schwarz inequality and entanglement in a two-mode three-level atomic system are investigated. It is shown that there are some states, which are entangled but do not violate Bell inequality in this system. Moreover, the relations of violations of Bell inequality, Cauchy—Schwarz inequality, and entanglement are discussed in detail.

We study the dynamic cavity method for dilute kinetic Ising models with synchronous update rules. For the parallel update rule we find for fully asymmetric models that the dynamic cavity equations reduce to a Markovian dynamics of the (time-dependent) marginal probabilities. For the random sequential update rule, also an instantiation of a synchronous update rule, we find on the other hand that the dynamic cavity equations do not reduce to a Markovian dynamics, unless an additional assumption of time factorization is introduced. For symmetric models we show that a fixed point of ordinary Belief propagation is also a fixed point of the dynamic cavity equations in the time factorized approximation. For clarity, the conclusions of the paper are formulated as three lemmas.

The transport property of electron through graphene-based double-barrier under a time periodic field is investigated. We study the influence of the system parameters and external field strength on the transmission probability. The results show that transmission exhibits various kinds of behavior with the change of parameters due to its angular anisotropy. One could control the values of transmission and conductivity as well as their distribution in each band by tuning the parameters.

The spin-3/2 Blume—Capel model is studied using the heating and cooling algorithms improved from the Creutz cellular automaton (CCA). The calculations are done on various sizes of the simple cubic lattice in the 0 ≤ D/J ≤ 5 parameter region. The phase diagram of the model and temperature variation of the thermodynamic quantities are obtained. We confirm the existence of a critical end point within the heating calculations. However, in contrast to the heating calculations, we do not obtain the first-order line at low temperature with cooling algorithm calculations. The results are compared with those of other theories.

Considering the attractive interaction between two magnons with opposite wave vectors in a Heisenberg ferromagnet, we propose the model of magnon-pairs, which is suitable for low-temperature environment. A dressed magnon is an energy quantum of the magnon-pairs whose energy is a monotonically increasing function of absolute temperature. Based on the model, we re-investigate the excitation mechanism and thermodynamic properties of the Heisenberg ferromagnet. The correction factor e(0) plays an important role in studying the low-temperature properties of a ferromagnet.

Different driving decisions will cause different processes of phase transition in traffic flow. To reveal the inner mechanism, this paper built a new cellular automaton (CA) model, based on the driving decision (DD). In the DD model, a driver's decision is divided into three stages: decision-making, action, and result. The acceleration is taken as a decision variable and three core factors, i.e. distance between adjacent vehicles, their own velocity, and the preceding vehicle's velocity, are considered. Simulation results show that the DD model can simulate the synchronized flow effectively and describe the phase transition in traffic flow well. Further analyses illustrate that various density will cause the phase transition and the random probability will impact the process. Compared with the traditional NaSch model, the DD model considered the preceding vehicle's velocity, the deceleration limitation, and a safe distance, so it can depict closer to the driver preferences on pursuing safety, stability and fuel-saving and has strong theoretical innovation for future studies.

In Verlinde's entropic force scenario of gravity, Newton's laws and Einstein equations can be obtained from the first principles and general assumptions. However, the equipartition law of energy is invalid at very low temperatures. We show clearly that the threshold of the equipartition law of energy is related with horizon of the universe. Thus, a one-dimensional Debye (ODD) model in the direction of radius of the modified entropic force (MEF) may be suitable in description of the accelerated expanding universe. We present a Friedmann cosmic dynamical model in the ODD-MEF framework. We examine carefully constraints on the ODD-MEF model from the Union2 compilation of the Supernova Cosmology Project (SCP) collaboration, the data from the observation of the large-scale structure (LSS) and the cosmic microwave background (CMB), i.e. SNe Ia+LSS+CMB. The combined numerical analysis gives the best-fit value of the model parameters ζ ≃ 10⁻⁹ and Ω_m0 = 0.224, with χ²_min = 591.156. The corresponding age of the universe agrees with the result of D. Spergel et al. [J.M. Bardeen, B. Carter, and S.W. Hawking, Commun. Math. Phys. 31 (1973) 161] at 95% confidence level. The numerical result also yields an accelerated expanding universe without invoking any kind of dark energy. Taking ζ(≡ 2πω_D/H₀) as a running parameter associated with the structure scale r, we obtain a possible unified scenario of the asymptotic flatness of the radial velocity dispersion of spiral galaxies, the accelerated expanding universe and the Pioneer 10/11 anomaly in the entropic force framework of Verlinde.

In the paper, we apply the weak gravity conjecture to the holographic quintessence model of dark energy. Three different holographic dark energy models are considered: without the interaction in the non-flat universe; with interaction in the flat universe; with interaction in the non-flat universe. We find that only in the models with the spatial curvature and interaction term proportional to the energy density of matter, it is possible for the weak gravity conjecture to be satisfied. And it seems that the weak gravity conjecture favors an open universe and the decaying of matter into dark energy.