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

Constraints on Unparticle Interactions from Invisible Decays of Z, Quarkonia and Neutrinos

Unparticles (\U) interact weakly with particles. The direct signature of unparticles will be in the form of missing energy. We study constraints on unparticle interactions using totally invisible decay modes of $Z$, vector quarkonia $V$ and neutrinos. The constraints on the unparticle interaction scale \Lambda_\U are very sensitive to the dimension d_\U of the unparticles. From invisible $Z$ and $V$ decays, we find that with d_\U close to 1 for vector \U, the unparticle scale \Lambda_\U can be more than $10^4$ TeV, and for d_\U around 2, the scale can be lower than one TeV. From invisible neutrino decays, we find that if d_\U is close to 3/2, the scale can be more than the Planck mass, but with d_\U around 2 the scale can be as low as a few hundred GeV. We also study the possibility of using V (Z)\to \gamma + \U to constrain unparticle interactions, and find that present data give weak constraints.Comment: 12 pages, 4 figures, version to appear in JHEP

Iterated Strict Dominance in General Games

We offer a definition of iterated elimination of strictly dominated strategies (IESDS) for games with (in)finite players, (non)compact strategy sets, and (dis)continuous payoff functions. IESDS is always a well-defined order independent procedure that can be used to solve Nash equilibrium in dominance-solvable games. We characterize IESDS by means of a "stability" criterion, and offer a sufficient and necessary epistemic condition for IESDS. We show by an example that IESDS may generate spurious Nash equilibria in the class of Reny's better-reply secure games. We provide sufficient/necessary conditions under which IESDS preserves the set of Nash equilibria. Nous donnons une définition de l’élimination itérative des stratégies qui sont strictement donimées (EISSD) pour les jeux avec un nombre fini (ou infini) de joueurs , des ensembles de stratégies compactes (ou non-compactes), et des fonctions de gains continues (ou non-continues). Le processus EISSD est bien défini et indépendant de l’ordre d’élimination. Nous donnons une caractérisation du processus EISSD en utilisant un critère de stabilité et offrons une condition épistémologique. Nous démontrons que le processus EISSD peut produire des équilibres faux dans la classe des jeux de meilleures réponses sécuritaires de Reny. Nous donnons des conditions nécessaires et suffisantes pour que le processus EISSD conserve l’ensemble des équilibre de Nash.game theory, strict dominance, iterated elimination, Nash equilibrium, Reny's better-reply secure games., théorie des jeux, dominance stricte, élimination itérative, équilibre de Nash, jeux de meilleures réponses sécuritaires de Reny

Zero-Shot Visual Recognition using Semantics-Preserving Adversarial Embedding Networks

We propose a novel framework called Semantics-Preserving Adversarial Embedding Network (SP-AEN) for zero-shot visual recognition (ZSL), where test images and their classes are both unseen during training. SP-AEN aims to tackle the inherent problem --- semantic loss --- in the prevailing family of embedding-based ZSL, where some semantics would be discarded during training if they are non-discriminative for training classes, but could become critical for recognizing test classes. Specifically, SP-AEN prevents the semantic loss by introducing an independent visual-to-semantic space embedder which disentangles the semantic space into two subspaces for the two arguably conflicting objectives: classification and reconstruction. Through adversarial learning of the two subspaces, SP-AEN can transfer the semantics from the reconstructive subspace to the discriminative one, accomplishing the improved zero-shot recognition of unseen classes. Comparing with prior works, SP-AEN can not only improve classification but also generate photo-realistic images, demonstrating the effectiveness of semantic preservation. On four popular benchmarks: CUB, AWA, SUN and aPY, SP-AEN considerably outperforms other state-of-the-art methods by an absolute performance difference of 12.2\%, 9.3\%, 4.0\%, and 3.6\% in terms of harmonic mean value

Nonlinear Hall response in the driving dynamics of ultracold atoms in optical lattices

We propose that a nonlinear Hall response can be observed in Bloch oscillations of ultracold atoms in optical lattices under the condition of preserved time-reversal symmetry. In the short-time limit of Bloch oscillations driven by a direct current (dc) field, the nonlinear Hall current dominates, being a second-order response to the external field strength. The associated Berry curvature dipole, which is a second-order nonlinear coefficient of the driving field, can be obtained from the oscillation of atoms. In an alternating current (ac) driving field, the nonlinear Hall response has a double frequency of the driving force in the case of time-reversal symmetry.Comment: 7 pages, 6 figure