Unusual behavior of sound velocity of a Bose gas in an optical superlattice at quasi-one-dimension

A Bose gas trapped in a one-dimensional optical superlattice has emerged as a novel superfluid characterized by tunable lattice topologies and tailored band structures. In this work, we focus on the propagation of sound in such a novel system and have found new features on sound velocity, which arises from the interplay between the two lattices with different periodicity and is not present in the case of a condensate in a monochromatic optical lattice. Particularly, this is the first time that the sound velocity is found to first increase and then decrease as the superlattice strength increases even at one dimension. Such unusual behavior can be analytically understood in terms of the competition between the decreasing compressibility and the increasing effective mass due to the increasing superlattice strength. This result suggests a new route to engineer the sound velocity by manipulating the superlattice's parameters. All the calculations based on the mean-field theory are justified by checking the exponent $\gamma$ of the off-diagonal one-body density matrix that is much smaller than 1. Finally, the conditions for possible experimental realization of our scenario are also discussed.Comment: 10 pages, 5 figure

On testing the equality of high dimensional mean vectors with unequal covariance matrices

In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problem in multivariate statistical analysis and there have been various tests proposed in the literature. Motivated by \citet{BaiS96E} and \cite{ChenQ10T}, a test statistic is introduced and the asymptomatic distributions under the null hypothesis as well as the alternative hypothesis are given. In addition, it is compared with a test statistic recently proposed by \cite{SrivastavaK13Ta}. It is shown that our test statistic performs much better especially in the large dimensional case

Bayesian Inference of the Specific Shear and Bulk Viscosities of the Quark-Gluon Plasma at Crossover from ϕ\phi and Ω\Omega Observables

Due to their weak final state interactions, the $\phi$ meson and $\Omega$ baryon provide unique probes of the properties of the quark-gluon plasma (QGP) formed in relativistic heavy-ion collisions. Using the quark recombination model with the quark phase-space information parameterized in a viscous blastwave, we study the transverse-momentum spectra and elliptic flows of $\phi$ and $\Omega$ in Au+Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV and Pb+Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV. The viscous blastwave includes non-equilibrium deformations of thermal distributions due to shear and bulk stresses and thus carries information on the specific shear viscosity $\eta/s$ and the specific bulk viscosity $\zeta/s$ of the QGP. We perform a model-to-data comparison with Bayesian inference and simultaneously obtain $\eta/s=(2.08^{+1.10}_{-1.09})/4\pi$ and $\zeta/s= 0.06^{+0.04}_{-0.04}$ at $90\%$ C.L. for the baryon-free QGP at crossover temperature of about $160$ MeV. Our work provides a novel approach to simultaneously determine the $\eta/s$ and $\zeta/s$ of the QGP at hadronization.Comment: 7 pages, 3 figures, 1 table. Presentation improved and discussions added. Accepted version to appear in PR