Self-Trapping of Bose-Einstein Condensates in an Optical Lattice: the Effect of the System Dimension

In the present paper, we investigate the dynamics of a Bose-Einstein condensates (BEC) loaded into an deep optical lattice of 1D, 2D and 3D, both analytically and numerically. We focus on the self-trapping state and the effect of the system dimension. Under the tight-binding approximation we obtain an analytical criterion for the self-trapping state of BEC using time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of the BEC cloud is obtained accordingly and verified by directly solving the discrete Gross-Pitaevskii equation (GPE) numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the lattices.Comment: 8pages, 9 figure

Search for C=+C=+ charmonium and XYZ states in e+e−→γ+He^+e^-\to \gamma+ H at BESIII

Within the framework of nonrelativistic quantum chromodynamics, we study the production of $C=+$ charmonium states $H$ in $e^+e^-\to \gamma~+~H$ at BESIII with $H=\eta_c(nS)$ (n=1, 2, 3, and 4), $\chi_{cJ}(nP)$ (n=1, 2, and 3), and $^1D_2(nD)$ (n=1 and 2). The radiative and relativistic corrections are calculated to next-to-leading order for $S$ and $P$ wave states. We then argue that the search for $C=+$ $XYZ$ states such as $X(3872)$, $X(3940)$, $X(4160)$, and $X(4350)$ in $e^+e^-\to \gamma~+~H$ at BESIII may help clarify the nature of these states. BESIII can search $XYZ$ states through two body process $e^+e^-\to \gamma H$, where $H$ decay to $J/\psi \pi^+\pi^-$, $J/\psi \phi$, or $D \bar D$. This result may be useful in identifying the nature of $C=+$ $XYZ$ states. For completeness, the production of $C=+$ charmonium in $e^+e^-\to \gamma +~H$ at B factories is also discussed.Comment: Comments and suggestions are welcome. References are update

Understanding the e+e−→D(∗)+D(∗)−e^+e^-\to D^{(*)+}D^{(*)-} processes observed by Belle

We calculate the production cross sections for $D^{*+}D^{*-}$, $D^+D^{*-}$ and $D^+D^-$ in $e^+e^-$ annihilation through one virtual photon in the framework of perturbative QCD with constituent quarks. The calculated cross sections for $D^{*+}D^{*-}$ and $D^+D^{*-}$ production are roughly in agreement with the recent Belle data. The helicity decomposition for $D^{*}$ meson production is also calculated. The fraction of the $D^{*\pm}_LD^{*\mp}_T$ final state in $e^+e^-\to D^{*+}D^{*-}$ process is found to be 65%. The fraction of $DD^*_T$ production is 100% and $DD^*_L$ is forbidden in $e^+e^-$ annihilation through one virtual photon. We further consider $e^+e^-$ annihilation through two virtual photons, and then find the fraction of $DD^{*}_T$ in $e^+e^-\to DD^{*}$ process to be about 91%.Comment: 8 pages, 2 figure