The dynamics of a certain density of interacting atoms arranged on a two-dimensional square lattice, which is made to slide over a two-dimensional periodic substrate potential with also the quare lattice symmetry, in the presence of dissipation, by an externally applied driving force, is studied. By rotating the misfit angle θ, the dynamical behaviour displays two different tribological regimes： one is smooth, the other becomes intermittent. We comment both on the nature of the atomic dynamics in the locked-to-sliding transition, and on the dynamical states displayed during the atom motion at different values of the driving force. In tribological applications, we also investigate how the main model parameters such as the stiffness strength and the magnitude of the adhesive force affect the static friction of the system. In particular, our simulation indicates that the superlubricity will appear.
By employing the quantum hydrodynamic model for electron ion dust plasma, we derive a dispersion relation of the quantum dusty plasma. The effects of the dust size distribution on the dispersion relation in a cold quantum dusty plasma are studied. Both analytical and numerical results are given to compare the differences between the dusty plasma by considering the dust size distribution and the mono-sized dusty plasma. It is shown that many system parameters can significantly influence the dispersion relation of the quantum dusty plasma.
By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova （FK） model with a square symmetry substrate potential for a square lattice layer has been investigated in this paper. For this system, the effects of many different parameters on the average velocity and the static friction force have been studied. It is found that not only the amplitude and frequency of ac-driven force, but also the direction of the external driving force and the misfit angle between two layers have some strong influences on the static friction force. It can be concluded that the superlubricity phenomenon appears easily with a larger ac amplitude and lower ac frequency for some special direction of the external force and misfit angle.
A one-dimensional （1D） Frenkel-Kontorova （FK） model is studied numerically in this paper, and two new analytical solutions （a supersonic kink and a nonlinear periodic wave） of the Sine-Gordon （SG） equation （continuum limit approximation of the FK model） are obtained by using the Jacobi elliptic function expansion method. Taking these new solutions as initial conditions for the FK model, we numerically find there exist the supersonic kink and the nonlinear periodic wave in these systems and obtain a lot of interesting and significant results. Moreover, we also investigate the subsonic kink and the breather in these systems and obtain some new feature.
We consider rotational motion of an interacting atomic Bose-Einstein condensate （BEC） with both two- and three- body interactions in a quadratic-plus-quartic and harmonic-plus-Gaussian trap. By using the variational method, the influence of the three-body interaction and the anharmonicity of the trap on the lowest energy surface mode excitation and the spontaneous shape deformation （responsible for the vortex formation） in a rotating BEC is discussed in detail. It is found that the repulsive three-body interaction helps the formation of the vortex and reduces the lowest energy surface mode frequency and the critical rotational frequency of the system. Moreover, the critical rotational frequency for the vortex formation in the harmonic-plus-Gaussian potential is lower than that in the quadratic-plus-quartic potential.
The effect of dust size distribution in ultracold quantum dusty plasmas are investigated in this paper. How the dispersion relation and the propagation velocity for the quantum dusty plasma vary with the system parameters and the different dust distribution are studied. It is found that as the Fermi temperature of the dust grains increases the frequency of the wave increases for large wave number dust acoustic wave. The quantum parameter of Hd also increases the frequency of the large wave number dust acoustic wave. It is also found that the frequency w0 and the propagation velocity v0 of quantum dust acoustic waves all increase as the total number density increases. They are greater for unusual dusty plasmas than those of the usual dusty plasma.
In this paper, we consider the macroscopic quantum tunnelling and self-trapping phenomena of Bose-Einstein condensates （BECs） with three-body recombination losses and atoms feeding from thermal cloud in triple-well potential. Using the three-mode approximation, three coupled Gross-Pitaevskii equations （GPEs）, which describe the dynamics of the system, are obtained. The corresponding numerical results reveal some interesting characteristics of BECs for different scattering lengths. The self-trapping and quantum tunnelling both are found in zero-phase and ：r-phase modes. Furthermore, we observe the quantum beating phenomenon and the resonance character during the self-trapping and quantum tunnelling. It is also shown that the initial phase has a significant effect on the dynamics of the system.
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.
