Annihilation Rates of Heavy 1−−1^{--} S-wave Quarkonia in Salpeter Method

The annihilation rates of vector $1^{--}$ charmonium and bottomonium $^3S_1$ states $V \rightarrow e^+e^-$ and $V\rightarrow 3\gamma$, $V \rightarrow \gamma gg$ and $V \rightarrow 3g$ are estimated in the relativistic Salpeter method. We obtained $\Gamma(J/\psi\rightarrow 3\gamma)=6.8\times 10^{-4}$ keV, $\Gamma(\psi(2S)\rightarrow 3\gamma)=2.5\times 10^{-4}$ keV, $\Gamma(\psi(3S)\rightarrow 3\gamma)=1.7\times 10^{-4}$ keV, $\Gamma(\Upsilon(1S)\rightarrow 3\gamma)=1.5\times 10^{-5}$ keV, $\Gamma(\Upsilon(2S)\rightarrow 3\gamma)=5.7\times 10^{-6}$ keV, $\Gamma(\Upsilon(3S)\rightarrow 3\gamma)=3.5\times 10^{-6}$ keV and $\Gamma(\Upsilon(4S)\rightarrow 3\gamma)=2.6\times 10^{-6}$ keV. In our calculations, special attention is paid to the relativistic correction, which is important and can not be ignored for excited $2S$, $3S$ and higher excited states.Comment: 10 pages,2 figures, 5 table

Power Efficient Visible Light Communication (VLC) with Unmanned Aerial Vehicles (UAVs)

A novel approach that combines visible light communication (VLC) with unmanned aerial vehicles (UAVs) to simultaneously provide flexible communication and illumination is proposed. To minimize the power consumption, the locations of UAVs and the cell associations are optimized under illumination and communication constraints. An efficient sub-optimal solution that divides the original problem into two sub-problems is proposed. The first sub-problem is modeled as a classical smallest enclosing disk problem to obtain the optimal locations of UAVs, given the cell association. Then, assuming fixed UAV locations, the second sub-problem is modeled as a min-size clustering problem to obtain the optimized cell association. In addition, the obtained UAV locations and cell associations are iteratively optimized multiple times to reduce the power consumption. Numerical results show that the proposed approach can reduce the total transmit power consumption by at least 53.8% compared to two baseline algorithms with fixed UAV locations.Comment: 4 pages, 4 figures. Accepted for publication in IEEE Communications Letter

Interaction effect in two-dimensional Dirac fermions

Based on the Dirac equations in the two-dimensional $\pi-$ flux model, we study the interaction effects both in nontrivial gapped and gapless Dirac equations with numerical exact diagonalization method. In the presence of the nearest and next nearest neighbor interactions: for nontrivial gapped Dirac equation, the topological phase is robust and persists in a finite region of the phase diagram; while for gapless Dirac equation, charge-density-wave and stripe phases are identified and the phase diagram in $(V_1, V_2)$ plane is obtained. When the next-next-nearest neighbor interaction is further included to gapless Dirac equation, the topological phase expected in the mean-field theory is absent. Our results are related to the possibility of dynamically generating topological phase from the electronic correlations.Comment: 7 pages, 8 figures. More discussins are added; accepted for publication in Physical Review