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

Emergent Dark Matter in Late Time Universe on Holographic Screen

We discuss a scenario that the dark matter in late time universe emerges as part of the holographic stress-energy tensor on the hypersurface in higher dimensional flat spacetime. Firstly we construct a toy model with a de Sitter hypersurface as the holographic screen in the flat bulk. After adding the baryonic matter on the screen, we assume that both of the dark matter and dark energy can be described by the Brown-York stress-energy tensor. From the Hamiltonian constraint equation in the flat bulk, we find an interesting relation between the dark matter and baryonic matter's energy density parameters, by comparing with the Lambda cold dark matter parameterization. We further compare this holographic embedding of emergent dark matter with traditional braneworld scenario and present an alternative interpretation as the holographic universe. It can be reduced to our toy constraint in the late time universe, with the new parameterization of the Friedmann equation. We also comment on the possible connection with Verlinde's emergent gravity, where the dark matter is treated as the elastic response of the baryonic matter on the de Sitter spacetime background. We show that from the holographic de Sitter model with elasticity, the Tully-Fisher relation and the dark matter distribution in the galaxy scale can be derived.Comment: 28 pages, 2 figures; Matches published version and we thank the referees for many insightful comments; v3: typos in the Friedmann equations are fixe

Bell Inequality in the Holographic EPR Pair

We study the Bell inequality in a holographic model of the casually disconnected Einstein-Podolsky-Rosen (EPR) pair. The Clauser-Horne-Shimony-Holt(CHSH) form of Bell inequality is constructed using holographic Schwinger-Keldysh (SK) correlators. We show that the manifestation of quantum correlation in Bell inequality can be holographically reproduced from the classical fluctuations of dual accelerating string in the bulk gravity. The violation of this holographic Bell inequality supports the essential quantum property of this holographic model of an EPR pair.Comment: 8 pages, 2 figures; references and texts added; v3: matches published versio

Petrov type I Condition and Rindler Fluid in Vacuum Einstein-Gauss-Bonnet Gravity

Recently the Petrov type I condition is introduced to reduce the degrees of freedom in the extrinsic curvature of a timelike hypersurface to the degrees of freedom in the dual Rindler fluid in Einstein gravity. In this paper we show that the Petrov type I condition holds for the solutions of vacuum Einstein-Gauss-Bonnet gravity up to the second order in the relativistic hydrodynamic expansion. On the other hand, if imposing the Petrov type I condition and Hamiltonian constraint on a finite cutoff hypersurface, the stress tensor of the relativistic Rindler fluid in vacuum Einstein-Gauss-Bonnet gravity can be recovered with correct first order and second order transport coefficients.Comment: 25 page