Table of contents

We propose a scheme to characterize the non-Markovian dynamics and quantify the non-Markovianity via the non-classicality measured by the negativity of quantumness. By considering a qubit in contact with a critical Ising spin bath and introducing an ancilla, we show that revivals of negativity of quantumness indicate the non-Markovian dynamics. Furthermore, a normalized measure of non-Markovianity based on the negativity of quantumness is introduced and the influences of bath criticality, bath temperature and bath size on the non-Markovianity are discussed. It is shown that, at the critical point, the decay of non-Markovianity versus the size of spin bath is the fastest and the non-Markovianity is exactly zero only in the thermodynamic limit. Besides, non-trivial behaviours of negativity of quantumness such as sudden change, double sudden changes and keeping constant are found for different relations between parameters of the initial state. Finally, how the non-classicality of the system is affected by a series of bang-bang pulses is also examined.

An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schrödinger (GNLS) equation, which can be reduced to classical discrete nonlinear Schrödinger (NLS) equation. Furthermore, all of the linear reductions for the discrete GNLS equation are given through the theory of circulant matrices and the discrete NLS equation is obtained by one of the reductions. At the same time, the recursion operator and symmetries of continuous GNLS equation are successfully recovered by its corresponding discrete ones.

The phenomena of cooperation in animal and human society are ubiquitous, but the selfish outcome that no player contributes to the public good will lead to the "tragedy of the commons". The recent research shows that high punishment can improve the cooperation of the population. In this paper, we introduce a punishment mechanism into spatial voluntary public goods games with every individual only knowing his own payoff in each round. Using the self-adjusting rules, we find that the different cost for punishment can lead to different effects on the voluntary public goods games. Especially, when the cost for punishment is decreased, a higher contribution region will appear in the case of low r value. It means even for the low r value, individuals can form the contributing groups in large quantities to produce a more efficient outcome than that in moderate r value. In addition, we also find the players' memory can have effects on the average outcome of the population.

We propose a scheme on control of the transition from quantum decoherence to coherence of a considered system S provided by the polarization degree of freedom of a probe field coupled to its motional degrees of freedom representing the environment B. A magneto-optically manipulated atomic ensemble with a tripod configuration is used to enhance the coupling between systems S and B. The spatial profile of the external fields induces a spatially varying potential for system B in the gas cell with identical and noninteracting atoms at different transverse points. It is found that the coherence of the system S can be maintained, lost or gained by properly choosing the incident positions of the probe field with respect to the center of the control laser field, and the two photon detuning for each components of the probe laser field.

In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed.

Finding the most robust entangled states during the whole process of decoherence is a particularly fundamental problem for quantum physics and quantum information processing. In this paper, the decoherence process of two-qubit system under two individual identical decoherence channels is investigated systematically. We find that although the robustness of two-qubit states with same initial entanglement is usually different, the Bell-like states are always the most robust entangled states during decoherence. That is to say, affected by the same amount of noise, the remain entanglement of an arbitrary two-qubit state is not more than that of a Bell-like state with the same initial entanglement.

We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205–1208]. Detailed examples are given to compute such invariant in detail. It is shown that these invariants can be used to detect the local unitary equivalence of degenerated quantum states.

In this paper, using relative entropy, we study monogamous properties of measurement-induced nonlocality based on relative entropy. Depending on different measurement sides, we provide necessary and sufficient conditions for two types of monogamy inequalities. By the concept of nonlocality monogamy score, we find a necessary condition of the vanished nonlocality monogamy score for arbitrary three-party states. In addition, two types of necessary and sufficient conditions of the vanished nonlocality monogamy scores are obtained for any pure states. As an application, we show that measurement-induced nonlocality based on relative entropy can be viewed as a "nonlocality witness" to distinguish generalized GHZ states from the generalized W states.

We present an efficient and simple protocol to unambiguously distinguish 2^N mutual orthogonal N-qubit Greenberger—Horne—Zeilinger states in polarization degree of freedom assisted by the frequency one. This scheme is based on N single photon Bell state measurements, which can be implemented non-locally. The success probability is 100% in principle and our scheme is feasible with current technology. All the advantages make our protocol meaningful and practical in quantum information processing.

Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.

In this paper we will analyze the third quantization of gravity in path integral formalism. We will use the time-dependent version of Wheeler—DeWitt equation to analyze the multiverse in this formalism. We will propose a mechanism for baryogenesis to occur in the multiverse, without violating the baryon number conservation.

We analytically study optical rogue waves in the presence of quintic nonlinearity and nonlinear dispersion effects. Dynamics of the rogue waves are investigated through the precise expressions of their peak, valley, trajectory, and width. Based on this, the properties of a few specific rogue waves are demonstrated in detail, and the dynamical evolution of rogue waves can be well controlled under different nonlinearity management. It shows that the peak reaches its maximum and the valley becomes minimized when the width evolves to the minimum value. Moreover, we find that the higher-order effects here achieve balance due to the integrability, and they only influence the rogue waves' trajectory.

Exact solutions with three-wave form including three solitary wave, breather-type two-solitary wave, doubly breather-type of solitary wave, double-periodic kind of solitary wave are obtained using bilinear form and extended three-wave approach with the aid of Maple. It is important that completed elastic collision, non-completed elastic collision, and fusion of three waves are investigated, respectively.

The pre-neutron-emission mass distributions for reaction ²³²Th(n, f) up to 60 MeV are systematically studied with an empirical fission potential model. The energy dependences of the peaks and valleys of the pre-neutron-emission mass distributions are described by the exponential expressions based on the newly measured data. The energy dependence of evaporation neutrons before scission, which plays a crucial role for the reasonable description of the mass distribution, is also considered. Both the double-humped and triple-humped shape of the measured pre-neutron-emission mass distributions for reaction ²³²Th(n, f) are reasonably well reproduced at incident energies up to 60 MeV. The mass distributions at unmeasured energies and the critical energies at which the humped pre-neutron-emission mass distributions are transformed into each other are also predicted.

The isoscaling and the isobaric yield ratio difference (IBD) probes, both of which are constructed by yield ratio of fragment, provide cancelation of parameters. The information entropy theory is introduced to explain the physical meaning of the isoscaling and IBD probes. The similarity between the isoscaling and IBD results is found, i.e., the information uncertainty determined by the IBD method equals to β – α determined by the isoscaling (α (β) is the parameter fitted from the isotopic (isotonic) yield ratio).

The entanglement of two qubits is investigated in the range of their ultra-strongly coupling with a quantum oscillator. The two qubits are initially in four Bell states and they are under the control mechanism of the coherent state of the quantum oscillator. There are four parameters: the average number of the coherent state, the ultra-strong coupling strength, the ratio of two frequencies of qubit and oscillator, and the inter-interaction coupling of the two qubits in the mechanism, and they all are influential parameters on the entanglement of the two qubits. One Bell state |0〉 is easyily kept and is trivial case. The novel results show that there is one state | I₀〉 among the other three Bell states which the entanglement of the two qubits could be almost completely preserved. The possibility is made into reality by the appropriate choice of the four influential parameters. We give two different schemes to choose the respective parameters to maintain the entanglment of | I₀〉 almost undiminished. The results will be useful for the quantum information process.

In this paper, we have studied discontinuity evolution and sonic propagation for the two-fluid model with small superfluid entropy in the framework of hydrodynamics. General features of the transverse mode and the longitudinal mode are provided. The fourth sound and the sixth sound are identified as the propagation of discontinuity, in agreement with earlier theoretical studies. Moreover, the growth equation is obtained to describe the decay and growth of the discontinuity propagating along its normal trajectory. The solution is in an integral form and various cases are discussed. Important discriminations between the case of fourth sound and that of sixth sound are also presented, which may be meaningful for future's experiments to identify the sixth sound and the small superfluid entropy.

A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier—Stokes equations, including contribution of chemical reaction, via the Chapman—Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed.

The multi-branched Husimi recursive lattice is extended to a virtual structure with fractional numbers of branches joined on one site. Although the lattice is undrawable in real space, the concept is consistent with regular Husimi lattice. The Ising spins of antiferromagnetic interaction on such a set of lattices are calculated to check the critical temperatures (T_c) and ideal glass transition temperatures (T_k) variation with fractional branch numbers. Besides the similar results of two solutions representing the stable state (crystal) and metastable state (supercooled liquid) and indicating the phase transition temperatures, the phase transitions show a well-defined shift with branch number variation. Therefore the fractional branch number as a parameter can be used as an adjusting tool in constructing a recursive lattice model to describe real systems.

The mutual coupling between neurons in a realistic neuronal system is much complex, and a two-layer neuronal network is designed to investigate the transition of electric activities of neurons. The Hindmarsh—Rose neuron model is used to describe the local dynamics of each neuron, and neurons in the two-layer networks are coupled in dislocated type. The coupling intensity between two-layer networks, and the coupling ratio (Pro), which defines the percentage involved in the coupling in each layer, are changed to observe the synchronization transition of collective behaviors in the two-layer networks. It is found that the two-layer networks of neurons becomes synchronized with increasing the coupling intensity and coupling ratio (Pro) beyond certain thresholds. An ordered wave in the first layer is useful to wake up the rest state in the second layer, or suppress the spatiotemporal state in the second layer under coupling by generating target wave or spiral waves. And the scheme of dislocation coupling can be used to suppress spatiotemporal chaos and excite quiescent neurons.

The main purpose of the present paper is to explore hypersurface homogenous space time in Brans Dicke theory of gravitation in terms of the dark energy source. To obtain solution of the field equation, we have taken into account the relation between ϕ and the average scale factor a. The volumetric expansions are considered to get deterministic solutions. Physical properties of the models are also discussed in detail.