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<jats:title>Abstract</jats:title> <jats:p>It has come to the attention of the Editors of Chinese Physics B that the article entitled 'Spatio-temporal of Dirac and Klein Gordon particles in a one-dimensional box' should not have been accepted for publication because of its substantial replication of a published article. Consequently, this paper has been withdrawn from publication.</jats:p>

<jats:p>We discuss the teleportation of particles in an environment of an <jats:italic>N</jats:italic>-body system. In this case, we can change a many-body system into an arbitrary shape in space by teleporting some or all the constituent particles, and thus we call the quantum teleportation under this circumstance as quantum tele-transformation (QTT). The particular feature of QTT is that the wave function of the internal degrees of freedom remains the same, while the spatial wave function experiences a drastic change. The notion of QTT provides conceptual and pedagogical convenience for quantum information processing. In view of QTT, teleportation is the change of a single particle in space, while entanglement swapping is the change of one particle of an entangled pair.</jats:p>

<jats:p>By means of composite quantum collision models, we study the entanglement dynamics of a bipartite system, i.e., two qubits <jats:italic>S</jats:italic> <jats:sub>1</jats:sub> and <jats:italic>S</jats:italic> <jats:sub>2</jats:sub> interacting directly with an intermediate auxiliary qubit <jats:italic>S</jats:italic> <jats:sub>A</jats:sub>, while <jats:italic>S</jats:italic> <jats:sub>A</jats:sub> is in turn coupled to a thermal reservoir. We are concerned with how the intracollisions of the reservoir qubits influence the entanglement dynamics. We show that even if the system is initially in the separated state, their entanglement can be generated due to the interaction between the qubits. In the long-time limit, the steady-state entanglement can be generated depending on the initial state of <jats:italic>S</jats:italic> <jats:sub>1</jats:sub> and <jats:italic>S</jats:italic> <jats:sub>2</jats:sub> and the environment temperature. We also study the dynamics of tripartite entanglement of the three qubits <jats:italic>S</jats:italic> <jats:sub>1</jats:sub>, <jats:italic>S</jats:italic> <jats:sub>2</jats:sub>, and <jats:italic>S</jats:italic> <jats:sub>A</jats:sub> when they are initially prepared in the GHZ state and separated state, respectively. For the GHZ initial state, the tripartite entanglement can be maintained for a long time when the collision strength between the environment qubits is sufficiently large.</jats:p>

<jats:p>We obtain the quantized momentum eigenvalues <jats:italic>P<jats:sub>n</jats:sub> </jats:italic> together with space-like coherent eigenstates for the space-like counterpart of the Schrödinger equation, the Feinberg–Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.</jats:p>

<jats:p>We investigate the non-Markovian effects on the entanglement transfer to the distant non-interacting atom qubits, which are embedded in a coupled superconducting resonator. The master equation governing the dynamics of the system is derived by the non-Markovian quantum state diffusion (NMQSD) method. Based on the solution, we show that the memory effect of the environment can lead to higher entanglement revival and make the entanglement last for a longer time. That is to say, the non-Markovian environment can enhance the entanglement transfer. It is also found that the maximum entanglement transferred to distant atoms can be modified by appropriately selecting the frequency of the modulated inter-cavity coupling. Moreover, with the initial anti-correlated state, the entanglement between the cavity fields can be almost completely transferred to the separated atoms. Lastly, we show that the memory effect has a significant impact on the generation of entanglement from the initial non-entangled states.</jats:p>

<jats:p>We investigate a two-level quantum system driven by a Lorentzian-shaped pulse field. An analytical solution is presented in terms of the confluent Heun functions. It is shown that for specially chosen parameter conditions, there are a number of the exact analytical solutions in an explicit form. The dependence of the final transition probabilities in the two levels on the system parameters is derived analytically and confirmed numerically.</jats:p>

<jats:p>We study a novel class of two-dimensional maps with infinitely many coexisting attractors. Firstly, the mathematical model of these maps is formulated by introducing a sinusoidal function. The existence and the stability of the fixed points in the model are studied indicating that they are infinitely many and all unstable. In particular, a computer searching program is employed to explore the chaotic attractors in these maps, and a simple map is exemplified to show their complex dynamics. Interestingly, this map contains infinitely many coexisting attractors which has been rarely reported in the literature. Further studies on these coexisting attractors are carried out by investigating their time histories, phase trajectories, basins of attraction, Lyapunov exponents spectrum, and Lyapunov (Kaplan–Yorke) dimension. Bifurcation analysis reveals that the map has periodic and chaotic solutions, and more importantly, exhibits extreme multi-stability.</jats:p>

<jats:p>We investigate rotational dynamics of an actively driven rotor through experiments and numerical simulations. While probability density distributions of rotor angular velocity are strongly non-Gaussian, relative probabilities of observing rotation in opposite directions are shown to be linearly related to the angular velocity magnitude. We construct a stochastic model to describe transitions between different states from rotor angular velocity data and use the stochastic model to show that symmetry properties in probability density distributions are related to the detailed fluctuation relation (FR) of entropy productions.</jats:p>

<jats:p>A two-dimensional detonation in H<jats:sub>2</jats:sub>–O<jats:sub>2</jats:sub> system is simulated by a high-resolution code based on the fifth-order weighted essentially non-oscillatory (WENO) scheme in the spatial discretization and the 3th-order additive Runge–Kutta schemes in the time discretization, by using a detailed chemical model. The effect of a concentration gradient on cellular detonation is investigated. The results show that with the increase of the concentration gradient, the cell instability of detonation increases and gives rise to the oscillation of average detonation velocity. After a long time, for the case of the lower gradient the detonation can be sustained, with the multi-head mode and single-head mode alternating, while for the higher gradient it propagates with a single-head mode.</jats:p>

<jats:p>Existing traffic flow models give little consideration on vehicle sizes. We introduce the solid angle into car-following theory, taking the driver’s perception of the leading vehicle’s size into account. The solid angle and its change rate are applied as inputs to the novel model. A nonlinear stability analysis is performed to analyze the asymmetry of the model and the size effect of the leading vehicle, and the modified Korteweg–de Vries equation is derived. The solid angle model can explain complex traffic characteristics and provide an important basis for modeling nonlinear traffic phenomena.</jats:p>