Entanglement Evolution of Two-Coupled Spins in a Time-Dependent Rotating Magnetic Field

We study the dynamics evolution of a two-qubit Heisenberg XXX spin chain under a time-dependent rotating magnetic field. Based on the algebraic structure of the non-autonomous system, the exact solution of the Schrodinger equation is obtained by using the method of algebraic dynamics. Based on the time-dependent analytical solution, we further study the entanglement evolution between the two coupled spins for different initial states, and find that the entanglement is determined by the coefficients of the initial state and the coupling constant J of the system.     

Dynamics of Rabi model under second-order Born Oppenheimer approximation

We apply the second-order Born–Oppenheimer(BO)approximation to investigate the dynamics of the Rabi model,which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approximation.By comparing with the numerical results,we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.     

Accelerating Consensus by Preferential Words in the Naming Game

The naming game is a model of nonequilibrium dynamics for the self-organized emergence of a language or a communication system. We study a modified version of the minimal naming game in which the speaker selects a word from its inventory with a probability proportional to exp（Rs ＊ α）, where Rs is the success ratio of the name and α is a tunable parameter. By investigating the effects of α on the evolutionary processes for both square lattice and scale-free networks, we find that the convergence time decreases with the increasing α on both two networks, which indicates that preferential selection of successful words can accelerate the reaching of consensus. More interestingly, for α 〉 0, we find that the relation between convergence time and α exhibits a power-law form.     

Coexistence and Extinction Pattern of Asymmetric Cyclic Game Species in a Square Lattice

The co-evolutionary dynamics of a cyclic game system is investigated in a two-dimensional square lattice with the asymmetrical rates for three species. Different with the well-mixed system, coexistence and extinction emerge alternately in the system, where a ＂zero-one＂ behavior is robust for a small population size, whereas, the system is predominated by coexistence for a big population one. We study in detail the influence about the fluctuation to the change of the state, and find that the difference between the maximal amplitude about the fluctuation and the average intensity determines which state the system is ultimately. In addition, we introduce Ports energy to explain the reason of the ＂zero-one＂ behavior. It is shown that the average Ports energy per site is the distance to the ＂zero-one＂ behavior in the model.     

Dynamical properties of two-band superlattices with strong interband coupling in real space under the action of ac and dc－ac fields

Within a two-band tight-binding model driven by ac and dc－ac electric fields, using numerical methods, we investigate the dynamics of electrons and the quasi-energy spectrum of the system with strong interband coupling in real space. We find that when the bandwidth is suppressed to a value much smaller than the field frequency, the dynamical localization can exist in the system. The corresponding regions are found for the occurrence of dynamical localization in the parameter space.     

Mean-Field Dynamics of a Two-Mode Bose-Einstein Condensate Subject to Decoherence

We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherenee （or particle loss）. Starting from the full many-body dynamics described by the master equation, an effective Gross- Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.     

Rotation of Bloch sphere induced by Lamb shift in open two-level systems

From a quite general form of the Lindblad-like master equation of open two-level systems(qubits), we study the effect of Lamb shift on the non-Markovian dynamics. We find that the Lamb shift can induce a non-uniform rotation of the Bloch sphere, but that it does not affect the non-Markovianity of the open system dynamics. We determine the optimal initial-state pairs that maximize the backflow of information for the considered master equation and find an interesting phenomenon–the sudden change of the non-Markovianity. We relate the dynamics to the evolution of the Bloch sphere to help us comprehend the obtained results.     

Enhancing entanglement generation of two atoms in a cavity with white noise using classical driving fields

We investigate the entanglement dynamics of a quantum system consisting of two two-level atoms in a cavity with classical driving fields in the presence of white noise.The cavity is initially prepared in the vacuum state.Generally,the entanglement of two atoms decreases with the intensity of the thermal fields and the coupling strength of the two-level atoms to the thermal fields.However,we find that the entanglement of the quantum system can be enhanced by adjusting the frequency and the strength of the classical driving fields in the presence of white noise.     

Self-trapping and Macroscopic Tunnelling of Superfluid Fermi Gases in Multi-well Potentials

We study the tunnelling dynamics of superfluid Fermi gases trapped in multi-well system along the BEC-BCS crossover. Within the hydrodynamical model and by using the multi-mode approximation, the self-trapping dynamics of superfluid Fermi gases in multi-well system are obtained numerically. We find that the self-trapping to diffusion transition strongly depends on the well number. When the well number is less than three, the self-trapped state takes place easier on the BEC side than that on the BCS side. However, when the well number is larger than three, the self-trapped state takes place easier on the BCS side instead of the BEC side. Furthermore, by considering a superfluid of 40K atoms, we obtain the zero-mode and π-mode Josephson frequencies of coherent atomic oscillations in double-well system. It is noteworthy that the Josephson mode, especially, the existence of π-mode frequency strongly depends on the atoms number on the BCS side.     

Bipartite Entanglement Dynamics in Three Qubits System with Dzyaloshinskii-Moriya Interaction

We investigate the bipartite entanglement dynamics of the system composed by three qubits A, B, and C. There is no interaction between A and B, and that of C and B is Dzyaloshinskii-Moriya （DM） spin-orbit interaction. We find that the purity of qubits A and B and the initial state of the qubit C are the two effective parameters to control the entanglement dynamics of the bipartite subsystems. This study sheds some lights on the control of quantum entanglement, which would be helpful for quantum information processing.     

Effect of Particle＇s Size on the Structural and Dynamical Properties in 2D Dusty Plasma

In a two-dimensional （219） dusty plasma system, the size of particles is considered under two different interparticle potentials （Yukawa potential and Dressed potential）. The structural and dynamical characters are investigated by molecular dynamics simulation respectively. The results show that the 2D systems via Yukawa and Dressed potentials have a different critical coupling constant F corresponding to the systems beginning to coagulate and exhibit different crystal configurations. Also we find that the size of particles has little influence on the 2D system＇s structure characters.     

Tunnelling Dynamics of Bose--Einstein Condensates in a Five-Well Trap

We develop a five-well model for describing the tunnelling dynamics of Bose-Einstein condensates （BECs） trapped in 2D optical lattices. The tunnelling dynamics of BECs in this five-well model are investigated both analytically and numerically. We focus on the self-trapped states and the difference of the tunnelling dynamics among two- well, three-well and five-well systems. The criterions for the self-trapped states and the phase diagrams of the five trapped BECs in zero-phase mode and π-phase mode are obtained. We find that the criterions and the phase diagrams are largely modified by the dimension of the system and the phase difference 5etween wells. The five-well model is a good model and can give us an insight into the tunnelling dynamics of BECs trapped in 2D optical lattices.     

Memory-Based Boolean Game and Self-Organized Phenomena on Networks

We study a memory-based Boolean game （MBBG） taking place on a regular ring, wherein each agent acts according to its local optimal states of the last M time steps recorded in memory, and the agents in the minority are rewarded. One free parameter p between 0 and 1 is introduced to denote the strength of the agent willing to make a decision according to its memory. It is found that giving proper willing strength p, the MBBG system can spontaneously evolve to a state of performance better than the random game; while for larger p, the herd behaviour emerges to reduce the system profit. By analysing the dependence of dynamics of the system on the memory capacity M, we find that a higher memory capacity favours the emergence of the better performance state, and effectively restrains the herd behaviour, thus increases the system profit. Considering the high cost of long-time memory, the enhancement of memory capacity for restraining the herd behaviour is also discussed, and M =5 is suggested to be a good choice.     

Entanglement dynamics of a moving multi-photon Jaynes-Cummings model in mixed states

Using the algebraic dynamical method,the entanglement dynamics of an atom-field bipartite system in a mixed state is investigated.The atomic center-of-mass motion and the field-mode structure are also included in this system.We find that the values of the detuning and the average photon number are larger,the amplitude of the entanglement is smaller,but its period does not increase accordingly.Moreover,with the increase of the field-mode structure parameter and the transition photon number,the amplitude of the entanglement varies slightly while the oscillation becomes more and more fast.Interestingly,a damping evolution of the entanglement appears when both the detuning and the atomic motion are considered simultaneously.     

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics.This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure.By constructing a proper Poincare map of the non-smooth system,an analytical expression of the Jacobian matrix of Poincare map is given.Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method.When the period is fixed and the coupling strength changes,the system undergoes stable,periodic,quasi-periodic,and hyper-chaotic solutions,etc.Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations.     

Interaction-Induced Characteristic Length in Strongly Many-Body Localized Systems

A complete set of local integrals of motion(LIOM) is a key concept for describing many-body localization(MBL),which explains a variety of intriguing phenomena in MBL systems.For example,LIOM constrain the dynamics and result in ergodicity violation and breakdown of the eigenstate thermalization hypothesis.However,it is difficult to find a complete set of LIOM explicitly and accurately in practice,which impedes some quantitative structural characterizations of MBL systems.Here we propose an accurate numerical method for constructing LIOM,discover through the LIOM an interaction-induced characteristic length +,and prove a ‘quasi-productstate' structure of the eigenstates with that characteristic length + for MBL systems.More specifically,we find that there are two characteristic lengths in the LIOM.The first one is governed by disorder and is of Andersonlocalization nature.The second one is induced by interaction but shows a discontinuity at zero interaction,showing a nonperturbative nature.We prove that the entanglement and correlation in any eigenstate extend not longer than twice the second length and thus the eigenstates of the system are the quasi-product states with such a localization length.     

Phase Propagations in a Coupled Oscillator-Excitor System of FitzHugh-Nagumo Models

A one-dimensional array of 2N ＋ 1 automata with FitzHugh-Nagumo dynamics, in which one is set to be oscillatory and the others are excitable, is investigated with hi-directional interactions. We find that 1 ： 1 rhythm propagation in the array depends on the appropriate couple strength and the excitability of the system. On the two sides of the 1 ： 1 rhythm area in parameter space, two different kinds of dynamical behaviour of the pacemaker, i.e. phase-locking phenomena and canard-like phenomena, are shown. The latter is found in company with chaotic pattern and period doubling bifurcation. When the coupling strength is larger than a critical value, the whole system ends to a steady state.     

Existence of horseshoe maps in voltage-mode controlled buck converters

In this paper, chaos in a voltage-mode controlled buck converter is studied. The existence of chaos is proven theoretically in this system. The proof consists of showing that the dynamics of the system is semiconjugate to that of a one-sided shift map, which implies positive entropy of the system and hence chaotic behaviour. The essential tool is the horseshoe hypotheses proposed by Kennedy and Yorke, which will be reviewed prior to the discussion of the main finding.     

Explosive synchronization in a mobile network in the presence of a positive feedback mechanism

Synchronization is a process that describes the coherent dynamics of a large ensemble of interacting units.The study of explosive synchronization transition attracts considerable attention.Here,I report the explosive transition within the framework of a mobile network,while each oscillator is controlled by global-order parameters of the system.Using numerical simulation,I find that the explosive synchronization(ES)transition behavior can be controlled by simply adjusting the fraction of controlled oscillators.The influences of some parameters on explosive synchronization are studied.Moreover,due to the presence of the positive feedback mechanism,I prevent the occurrence of the synchronization of continuous-phase transition and make phase transition of the system a first-order phase transition accompanied by a hysteresis loop.