In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G'/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.

In this paper, we use entangled states to construct 9 × 9-matrix representations of Temperley—Lieb algebra (TLA), then a family of 9 × 9-matrix representations of Birman—Wenzl—Murakami algebra (BWMA) have been presented. Based on which, three topological basis states have been found. And we apply topological basis states to recast nine-dimensional BWMA into its three-dimensional counterpart. Finally, we find the topological basis states are spin singlet states in special case.

The max-min approach is applied to mathematical models of some nonlinear oscillations. The models are regarding to three different forms that are governed by nonlinear ordinary differential equations. In this context, the strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration. The obtained results via the approach are compared with ones achieved utilizing other techniques. The results indicate that the approach has a good agreement with other well-known methods. He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.

We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen—Cooper—Schrieffer (BCS) superfluid to Bose—Einstein condensates (BEC). Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the case of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.

Quantum entanglement dynamics for two atoms trapped in two coupled cavities is investigated. Numerical results show that the present of the two atomic excitations is mainly accounted for the entanglement-sudden-death (ESD) effect with the two cavities initially in the vacuum. The entanglement can also be controlled by the hopping rate and the imbalances between the two atom-cavity coupling rates.

In this article, we derive the explicit entanglement and fidelity expressions for a larger class of two-qubit states, namely, a seven-parameter family of so called X-states. The analytical expressions of the entanglement, the output entanglement and the average fidelity are obtained for this general model by using the concept of concurrence and average fidelity. We study the relations between quantum entanglement, the output entanglement, and the average fidelity for standard teleportation of one-qubit and partial teleportation of two-qubit state. We discover that the average fidelity and entanglement is not a simple dependence relation. The higher entangled system is helpful for teleportation.

We propose a one-step method to prepare multi-qubit GHZ and W states with transmon qubits capacitively coupled to a superconducting transmission line resonator (TLR). Compared with the scheme firstly introduced by Wang et al. [ Phys. Rev. B 81 (2010) 104524], our schemes have longer dephasing time and much shorter operation time because the transmon qubits we used are not only more robust to the decoherence and the unavoidable parameter variations, but also have much stronger coupling constant with TLR. Based on the favourable properties of transmons and TLR, our method is more feasible in experiment.

We study the entropy correlations between subsystems in a bipartite system. Our results show that there is an entropy exchange effect (i.e., anticorrelation phenomenon) between atom and field. Especially we prove that there exists a condition for complete entropy exchange between atom and field.

The Feshbach—Rubinow approximation and its improved versions have been applied to the H ⁺ ₂ ion system. The ground-state energies are calculated with these different methods. The best ground-state energy obtained is only 2% higher than the experimental result. Given the simplicity of the method, this accuracy is quite remarkable. It is shown that the screening effect plays a less significant role and the effective potential between the two protons is probably of most importance in this problem.

In this paper, the bilinear form of a generalized Kadomtsev—Petviashvili equation is obtained by applying the binary Bell polynomials. The N-soliton solution and one periodic wave solution are presented by use of the Hirota direct method and the Riemann theta function, respectively. And then the asymptotic analysis demonstrates one periodic wave solution can be reduced to one soliton solution. In the end, the bilinear Bäcklund transformations are derived.