Conformal Ricci flow on asymptotically hyperbolic manifolds

In this article we study the short-time existence of conformal Ricci flow on asymptotically hyperbolic manifolds. We also prove a local Shi's type curvature derivative estimate for conformal Ricci flow.Comment: 19 pages. No figur

New Insights on Low Energy πN\pi N Scattering Amplitudes

The $S$- and $P$- wave phase shifts of low-energy pion-nucleon scatterings are analysed using Peking University representation, in which they are decomposed into various terms contributing either from poles or branch cuts. We estimate the left-hand cut contributions with the help of tree-level perturbative amplitudes derived in relativistic baryon chiral perturbation theory up to $\mathcal{O}(p^2)$. It is found that in $S_{11}$ and $P_{11}$ channels, contributions from known resonances and cuts are far from enough to saturate experimental phase shift data -- strongly indicating contributions from low lying poles undiscovered before, and we fully explore possible physics behind. On the other side, no serious disagreements are observed in the other channels.Comment: slightly chnaged version, a few more figures added. Physical conclusions unchange

Luttinger-volume violating Fermi liquid in the pseudogap phase of the cuprate superconductors

Based on the NMR measurements on Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ (La-Bi2201) in strong magnetic fields, we identify the non-superconducting pseudogap phase in the cuprates as a Luttinger-volume violating Fermi liquid (LvvFL). This state is a zero temperature quantum liquid that does not break translational symmetry, and yet, the Fermi surface encloses a volume smaller than the large one given by the Luttinger theorem. The particle number enclosed by the small Fermi surface in the LvvFL equals the doping level $p$, not the total electron number $n_e=1-p$. Both the phase string theory and the dopon theory are introduced to describe the LvvFL. For the dopon theory, we can obtain a semi-quantitative agreement with the NMR experiments.Comment: The final version in PR

Phoebe's orbit from ground-based and space-based observations

The ephemeris of Phoebe, the ninth satellite of Saturn, is not very accurate. Previous dynamical models were usually too simplified, the astrometry is heterogeneous and, the Saturn's ephemeris itself is an additionnal source of error. The aim is to improve Phoebe's ephemeris by using a large set of observations, correcting some systematic errors and updating the dynamical model. The dynamical model makes use of the most recent ephemeris of planets and Saturnian satellites. The astrometry of Phoebe is improved by using a compilation of ground-based and space-based observations and by correcting the bias in stellar catalogues used for the reduction. We present an accurate ephemeris of Phoebe with residuals of 0.45 arcsec and with an estimated accuracy of Phoebe's position of less that 100 km on 1990-2020 period.Comment: 10 pages, 9 figures, accepted by A&