Induced modification of geometric phase of a qubit coupled to an XY spin chain by the Dzyaloshinsky–Moriya interaction

We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya (DM) interaction in the presence of a transverse magnetic field. An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit. We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by the DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain.     

Exact solutions of an Ising spin chain with a spin-1 impurity

An exact solution of a single impurity model is hard to derive since it breaks translation invariance symmetry. We present the exact solution of the spin-1/2 transverse Ising chain imbedded by a spin-1 impurity. Using the hole decomposition scheme, we exactly solve the spin-1 impurity in two subspaces which are generated by a conserved hole operator.The impurity enlarges the energy deformation of the ground state above a pure transverse Ising system without impurity.The specific heat coefficient shows a small anomaly at low temperature for finite size. This indicates that the impurity can tune the ground state from a magnetic impurity space to a non-magnetic impurity space, which only exists for spin-1impurity comparing with spin-1/2 impurity and a pure transverse Ising chain without impurity. These behaviors essentially come from adding impurity freedom, which induces a competition between hole and fermion excitation depending on the coupling strength with its neighbor and the single-ion anisotropy.     

Dark Solitons in FPU Lattice Chain

Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton. Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.     

Computer-assisted analysis of chaos in a three-species food chain model

In this paper, a three-species food chain model with Holling type IV and Beddington–DeAngelis functional responses is formulated. Numerical simulations show that this system can generate chaos for some parameter values. But the mechanism behind chaos is still unclear only through numerical simulations. Then, using the topological horseshoe theories and Conley–Moser conditions, we present a computer-assisted analysis to show the chaoticity of this system in the topological sense, that is, it has positive topological entropy. We prove that the Poincaré map of this model possesses a closed uniformly hyperbolic chaotic invariant set, and it is topologically conjugate to a 2-shift map. At last, we consider the impact of fear on this three-species model. It is an important factor in controlling chaos in biological models, which has been validated in other models.      

Virial expansion for a polymer with a realistic pair-potential interaction

No modern theory of polymer excluded volume adequately describes the crossover from poor solvent to good solvent conditions; a fundamental difficulty is a singularity in the binary cluster integral. Mayer expansion techniques are applied to a model with a pair interaction between monomers to clarify the distinction between geometric and solvent contributions to excluded volume. Detailed calculations are undertaken for a hard-core potential and a mimic Lennard-Jones potential. The significance of the singularity in the binary cluster integral for calculations in the crossover regime is discussed.     

次近邻相互作用对Heisenberg XX链纠缠影响的研究

研究了存在次近邻相互作用(耦合)时Heisenberg XX链的纠缠特性. 结果表明对近邻格点, 随着耦合常数J的变化, 次近邻相互作用的存在可能使其纠缠度增大或者减小; 而对次近邻格点, 引进次近邻相互作用却可以产生纠缠, 并且使其随着|J|的增大而增大. 近邻格点间纠缠存在的临界温度T_c随着J的增大而降低, 次近邻格点间纠缠存在的临界温度T_c随着|J|的增大而升高. 此外对纠缠W态的制备, 次近邻相互作用的存在还使得三量子位情形时W态产生的时刻改变, 而对于四量子位情形却没有影响.     

双轴压缩下颗粒物质剪切带的形成与发展

本文采用离散元方法,研究了双轴压缩的颗粒体系在刚性边界约束下,局部剪切带的形成和发展过程,注重分析了细观的体积分数、配位数、颗粒旋转角度等参数以及力链结构形态的演变.并从颗粒体系jamming 相图中J点附近的边壁压强和配位数随体积分数的标度规律出发,分析了剪切带内外的体积分数和配位数的变化.结果表明:剪切带形成于颗粒体系的塑性变形开始阶段,此时体系发生剪胀,颗粒体积分数减小,颗粒体系抵抗旋转的能力降低,开始出现细小剪切带,随着轴向应变的继续,细小剪切带发生连接,最终导致贯穿性优势剪切带形成 关键词： 颗粒物质 力链 双轴压缩 剪切带     

自由边界双原子链的晶格振动

指出双原子的晶格振动分为声学支和光学支是由于采用循环边界条件所造成的结果，若采用自由边界条件，则模花样和振动频谱完全不同，这时只能分为低频支，中频支和高频支。     

Spin-gapped phases in the frustrated Hubbard chain with transverse spin anisotropy

At weak coupling, we investigate the frustrated Hubbard chain including nearest-neighbor and next-nearest-neighbor antiferromagnetic exchange with easy-plane anisotropy $J_1^{xy}$ and $J_2^{xy}$. At half filling, we obtain three different phases in the $J_1^{xy}$–${J_2}^{xy}$ plane: a transverse spin density wave phase, a bond order wave phase and a Luther–Emery metallic phase characterized by the coexistence of singlet superconductivity and charge density wave correlations. The frustrating exchange $J_2^{xy}$ accounts for the spin-gapped phases.     

Consensus protocol for heterogeneous multi-agent systems: A Markov chain approach

This paper deals with the consensus problem for heterogeneous multi-agent systems. Different from most existing consensus protocols, we consider the consensus seeking of two types of agents, namely, active agents and passive agents. The objective is to directly control the active agents such that the states of all the agents would achieve consensus. In order to obtain a computational approach, we subtly introduce an appropriate Markov chain to cast the heterogeneous systems into a unified framework. Such a framework is helpful for tackling the constraints from passive agents. Furthermore, a sufficient and necessary condition is established to guarantee the consensus in heterogeneous multi-agent systems. Finally, simulation results are provided to verify the theoretical analysis and the effectiveness of the proposed protocol.