Collective modes of a harmonically trapped one-dimensional Bose gas: the effects of finite particle number and nonzero temperature

Following the idea of the density functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap, by using a local chemical potential - calculated with the Lieb-Liniger exact solution - as the exchange energy. At zero temperature, we use the theory to describe collective modes of a finite-particle system in all interaction regimes from the ideal gas limit, to the mean-field Thomas-Fermi regime, and to the strongly interacting Tonks-Girardeau regime. At finite temperature, we investigate the temperature dependence of collective modes in the weak-coupling regime by means of a Hartree-Fock-Bogoliubov theory with Popov approximation. By emphasizing the effects of finite particle number and nonzero temperature on collective mode frequencies, we make comparisons of our results with the recent experimental measurement [E. Haller et al., Science 325, 1224 (2009)] and some previous theoretical predictions. We show that the experimental data are still not fully explained within current theoretical framework.Comment: 10 pages, 8 figure

Possible singlet and triplet superconductivity on honeycomb lattice

We study the possible superconducting pairing symmetry mediated by spin and charge fluctuations on the honeycomb lattice using the extended Hubbard model and the random-phase-approximation method. From $2\%$ to $20\%$ doping levels, a spin-singlet $d_{x^{2}-y^{2}}+id_{xy}$-wave is shown to be the leading superconducting pairing symmetry when only the on-site Coulomb interaction $U$ is considered, with the gap function being a mixture of the nearest-neighbor and next-nearest-neighbor pairings. When the offset of the energy level between the two sublattices exceeds a critical value, the most favorable pairing is a spin-triplet $f$-wave which is mainly composed of the next-nearest-neighbor pairing. We show that the next-nearest-neighbor Coulomb interaction $V$ is also in favor of the spin-triplet $f$-wave pairing.Comment: 6 pages, 4 figure

Video Question Answering via Attribute-Augmented Attention Network Learning

Video Question Answering is a challenging problem in visual information retrieval, which provides the answer to the referenced video content according to the question. However, the existing visual question answering approaches mainly tackle the problem of static image question, which may be ineffectively for video question answering due to the insufficiency of modeling the temporal dynamics of video contents. In this paper, we study the problem of video question answering by modeling its temporal dynamics with frame-level attention mechanism. We propose the attribute-augmented attention network learning framework that enables the joint frame-level attribute detection and unified video representation learning for video question answering. We then incorporate the multi-step reasoning process for our proposed attention network to further improve the performance. We construct a large-scale video question answering dataset. We conduct the experiments on both multiple-choice and open-ended video question answering tasks to show the effectiveness of the proposed method.Comment: Accepted for SIGIR 201