On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties

Let f : X --> X be a dominant rational map of a projective variety defined over a global field, let d_f be the dynamical degree of f, and let h_X be a Weil height on X relative to an ample divisor. We prove that h_X(f^n(P)) << (d_f + e)^n h_X(P), where the implied constant depends only on X, h_X, f, and e. As applications, we prove a fundamental inequality a_f(P) \le d_f for the upper arithmetic degree and we construct canonical heights for (nef) divisors. We conjecture that a_f(P) = d_f whenever the orbit of P is Zariski dense, and we describe some cases for which we can prove our conjecture.Comment: 32 page

Experimental evidence of TcT_c enhancement without the influence of spin fluctuations: NMR study on LaFeAsO_{1-x}H_x under a pressure of 3.0 GPa

The electron-doped high-transition-temperature (T_c) iron-based pnictide superconductor LaFeAsO_{1-x}H_x has a unique phase diagram: superconducting (SC) double domes are sandwiched by antiferromagnetic phases at ambient pressure and they turn to a single dome with a maximum T_c that exceeds 45K at a pressure of 3.0 GPa. We studied whether spin fluctuations are involved in increasing T_c under a pressure of 3.0 GPa by using ^{75}As nuclear magnetic resonance (NMR) technique. The ^{75}As-NMR results for the powder samples show that T_c increases up to 48 K without the influence of spin fluctuations. The fact indicates that spin fluctuations are not involved in raising T_c, which implies that other factors, such as orbital degrees of freedom, may be important for achieving a high T_c of almost 50 K.Comment: Correponding Author: Naoki Fujiwar

Friction, order, and transverse pinning of a two-dimensional elastic lattice under periodic and impurity potentials

Frictional phenomena of two-dimensional elastic lattices are studied numerically based on a two-dimensional Frenkel-Kontorova model with impurities. It is shown that impurities can assist the depinning. We also investigate anisotropic ordering and transverse pinning effects of sliding lattices, which are characteristic of the moving Bragg glass state and/or transverse glass state. Peculiar velocity dependence of the transverse pinning is observed in the presence of both periodic and random potentials and discussed in the relation with growing order and discommensurate structures.Comment: RevTeX, 4 pages, 5 figures. to appear in Phys. Rev. B Rapid Commu