Eigenvalues of Curvature, Lyapunov exponents and Harder-Narasimhan filtrations

Inspired by Katz-Mazur theorem on crystalline cohomology and by Eskin-Kontsevich-Zorich's numerical experiments, we conjecture that the polygon of Lyapunov spectrum lies above (or on) the Harder-Narasimhan polygon of the Hodge bundle over any Teichm\"uller curve. We also discuss the connections between the two polygons and the integral of eigenvalues of the curvature of the Hodge bundle by using Atiyah-Bott, Forni and M\"oller's works. We obtain several applications to Teichm\"uller dynamics conditional to the conjecture.Comment: 37 pages. We rewrite this paper without changing the mathematics content. arXiv admin note: text overlap with arXiv:1112.5872, arXiv:1204.1707 by other author

The pole structure of low energy πN\pi N scattering amplitudes

This report presents an investigation of the pion-nucleon elastic scattering in low energy region using a production representation of the partial wave $S$ matrix. The phase shifts are separated into contributions from poles and branch cuts, where the left-hand cut term can be evaluated by tree-level covariant baryon chiral perturbation theory. A comparison between the sum of known contributions and the data in $S$- and $P$- wave channels is made. It is found that the known components in $S_{11}$ and $P_{11}$ channels are far from enough to saturate the corresponding experimental data, indicating the existence of low-lying hidden poles. The positions of those hidden poles are figured out and the physics behind them are explored.Comment: 5 pages. Conference proceeding of 15th International Workshop on Meson Physics, Cracow, Poland, 7th-12th June 201

QCD phase transitions via a refined truncation of Dyson-Schwinger equations

We investigate both the chiral and deconfinement phase transitions of QCD matter in a refined scheme of Dyson-Schwinger equations, which have been shown to be successful in giving the meson mass spectrum and matching the interaction with the results from ab initio computation. We verify the equivalence of the chiral susceptibility criterion with different definitions for the susceptibility and confirm that the chiral susceptibility criterion is efficient to fix not only the chiral phase boundary but also the critical end point (CEP), especially when one could not have the effective thermodynamical potential. We propose a generalized Schwinger function criterion for the confinement. We give the phase diagram of both phase transitions and show that in the refined scheme the position of the CEP shifts to lower chemical potential and higher temperature. Based on our calculation and previous results of the chemical freeze out conditions, we propose that the CEP locates in the states of the matter generated by the Au--Au collisions with $\sqrt{s_{NN}^{}}=9\sim15$ GeV.Comment: 12 pages, 6 figures, 1 tabl