Dynamical properties of a trapped dipolar Fermi gas at finite temperature

We investigate the dynamical properties of a trapped finite-temperature normal Fermi gas with dipole-dipole interaction. For the free expansion dynamics, we show that the expanded gas always becomes stretched along the direction of the dipole moment. In addition, we present the temperature and interaction dependences of the asymptotical aspect ratio. We further study the collapse dynamics of the system by suddenly increasing the dipolar interaction strength. We show that, in contrast to the anisotropic collapse of a dipolar Bose-Einstein condensate, a dipolar Fermi gas always collapses isotropically when the system becomes globally unstable. We also explore the interaction and temperature dependences for the frequencies of the low-lying collective excitations.Comment: 11 pages, 7 figure

A Deep Relevance Matching Model for Ad-hoc Retrieval

In recent years, deep neural networks have led to exciting breakthroughs in speech recognition, computer vision, and natural language processing (NLP) tasks. However, there have been few positive results of deep models on ad-hoc retrieval tasks. This is partially due to the fact that many important characteristics of the ad-hoc retrieval task have not been well addressed in deep models yet. Typically, the ad-hoc retrieval task is formalized as a matching problem between two pieces of text in existing work using deep models, and treated equivalent to many NLP tasks such as paraphrase identification, question answering and automatic conversation. However, we argue that the ad-hoc retrieval task is mainly about relevance matching while most NLP matching tasks concern semantic matching, and there are some fundamental differences between these two matching tasks. Successful relevance matching requires proper handling of the exact matching signals, query term importance, and diverse matching requirements. In this paper, we propose a novel deep relevance matching model (DRMM) for ad-hoc retrieval. Specifically, our model employs a joint deep architecture at the query term level for relevance matching. By using matching histogram mapping, a feed forward matching network, and a term gating network, we can effectively deal with the three relevance matching factors mentioned above. Experimental results on two representative benchmark collections show that our model can significantly outperform some well-known retrieval models as well as state-of-the-art deep matching models.Comment: CIKM 2016, long pape

Event-by-event shape and flow fluctuations of relativistic heavy-ion collision fireballs

Heavy-ion collisions create deformed quark-gluon plasma (QGP) fireballs which explode anisotropically. The viscosity of the fireball matter determines its ability to convert the initial spatial deformation into momentum anisotropies that can be measured in the final hadron spectra. A quantitatively precise empirical extraction of the QGP viscosity thus requires a good understanding of the initial fireball deformation. This deformation fluctuates from event to event, and so does the finally observed momentum anisotropy. We present a harmonic decomposition of the initial fluctuations in shape and orientation of the fireball and perform event-by-event ideal fluid dynamical simulations to extract the resulting fluctuations in the magnitude and direction of the corresponding harmonic components of the final anisotropic flow at midrapidity. The final harmonic flow coefficients are found to depend non-linearly on the initial harmonic eccentricity coefficients. We show that, on average, initial density fluctuations suppress the buildup of elliptic flow relative to what one obtains from a smooth initial profile of the same eccentricity, and discuss implications for the phenomenological extraction of the QGP shear viscosity from experimental elliptic flow data.Comment: 22 pages, 17 figures. Relative to [v2], minor changes in text. Fig. 9 redrawn. This version accepted by Phys. Rev.

Density oscillations in trapped dipolar condensates

We investigated the ground state wave function and free expansion of a trapped dipolar condensate. We find that dipolar interaction may induce both biconcave and dumbbell density profiles in, respectively, the pancake- and cigar-shaped traps. On the parameter plane of the interaction strengths, the density oscillation occurs only when the interaction parameters fall into certain isolated areas. The relation between the positions of these areas and the trap geometry is explored. By studying the free expansion of the condensate with density oscillation, we show that the density oscillation is detectable from the time-of-flight image.Comment: 7 pages, 9 figure

On several families of elliptic curves with arbitrary large Selmer groups

In this paper, we calculate the $\phi (\hat{\phi})-$Selmer groups S^{(\phi)} (E / \Q) and S^{(\hat{\varphi})} (E^{\prime} / \Q) of elliptic curves $y^{2} = x (x + \epsilon p D) (x + \epsilon q D)$ via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be arbitrary large.Comment: 22 page

Persistent global power fluctuations near a dynamic transition in electroconvection

This is a study of the global fluctuations in power dissipation and light transmission through a liquid crystal just above the onset of electroconvection. The source of the fluctuations is found to be the creation and annihilation of defects. They are spatially uncorrelated and yet temporally correlated. The temporal correlation is seen to persist for extremely long times. There seems to be an especially close relation between defect creation/annihilat ion in electroconvection and thermal plumes in Rayleigh-B\'enard convection

The structures of Hausdorff metric in non-Archimedean spaces

For non-Archimedean spaces $X$ and $Y,$ let $\mathcal{M}_{\flat } (X), \mathfrak{M}(V \rightarrow W)$ and $\mathfrak{D}_{\flat }(X, Y)$ be the ballean of $X$ (the family of the balls in $X$), the space of mappings from $X$ to $Y,$ and the space of mappings from the ballen of $X$ to $Y,$ respectively. By studying explicitly the Hausdorff metric structures related to these spaces, we construct several families of new metric structures (e.g., $\widehat{\rho } _{u}, \widehat{\beta }_{X, Y}^{\lambda }, \widehat{\beta }_{X, Y}^{\ast \lambda }$) on the corresponding spaces, and study their convergence, structural relation, law of variation in the variable $\lambda,$ including some normed algebra structure. To some extent, the class $\widehat{\beta }_{X, Y}^{\lambda }$ is a counterpart of the usual Levy-Prohorov metric in the probability measure spaces, but it behaves very differently, and is interesting in itself. Moreover, when $X$ is compact and $Y = K$ is a complete non-Archimedean field, we construct and study a Dudly type metric of the space of $K-$valued measures on $X.$Comment: 43 pages; this is the final version. Thanks to the anonymous referee's helpful comments, the original Theorem 2.10 is removed, Proposition 2.10 is stated now in a stronger form, the abstact is rewritten, the Monna-Springer is used in Section 5, and Theorem 5.2 is written in a more general for