A convergent method for linear half-space kinetic equations

We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both analysis and numerics includes three steps: adding damping terms to the original half-space equation, using an inf-sup argument and even-odd decomposition to establish the well-posedness of the damped equation, and then recovering solutions to the original half-space equation. The proposed numerical methods for the damped equation is shown to be quasi-optimal and the numerical error of approximations to the original equation is controlled by that of the damped equation. This efficient solution to the half-space problem is useful for kinetic-fluid coupling simulations

The Υ(nS){\Upsilon}(nS) →{\to} Bc∗πB_{c}^{\ast}{\pi}, Bc∗KB_{c}^{\ast}K decays with perturbative QCD approach

Besides the traditional strong and electromagnetic decay modes, ${\Upsilon}(nS)$ meson can also decay through the weak interactions within the standard model of elementary particle. With anticipation of copious ${\Upsilon}(nS)$ data samples at the running LHC and coming SuperKEKB experiments, the two-body nonleptonic bottom-changing ${\Upsilon}(nS)$ ${\to}$ $B_{c}^{\ast}{\pi}$, $B_{c}^{\ast}K$ decays ($n$ $=$ 1, 2, 3) are investigated with perturbative QCD approach firstly. The absolute branching ratios for ${\Upsilon}(nS)$ ${\to}$ $B_{c}^{\ast}{\pi}$ and $B_{c}^{\ast}K$ decays are estimated to reach up to about $10^{-10}$ and $10^{-11}$, respectively, which might possibly be measured by the future experiments.Comment: 16 pages, 3 figure

Transfer-matrix renormalization group study of the spin ladders with cyclic four-spin interactions

The temperature dependence of the specific heat and spin susceptibility of the spin ladders with cyclic four-spin interactions in the rung-singlet phase is explored by making use of the transfer-matrix renormalization group method. The values of spin gap are extracted from the specific heat and susceptibility, respectively. It is found that for different relative strength between interchain and intrachain interactions, the spin gap is approximately linear with the cyclic four-spin interaction in the region far away from the critical point. Furthermore, we show that the dispersion for the one-triplet magnon branch can be obtained by numerically fitting on the partition function.Comment: 7 pages, 7 figures, 1 tabl