Isotrivial VMRT-structures of complete intersection type

The family of varieties of minimal rational tangents on a quasi-homogeneous projective manifold is isotrivial. Conversely, are projective manifolds with isotrivial varieties of minimal rational tangents quasi-homogenous? We will show that this is not true in general, even when the projective manifold has Picard number 1. In fact, an isotrivial family of varieties of minimal rational tangents needs not be locally flat in differential geometric sense. This leads to the question for which projective variety Z, the Z-isotriviality of varieties of minimal rational tangents implies local flatness. Our main result verifies this for many cases of Z among complete intersections.Comment: Some errors in Section 8 and Lemma 8.1 corrected. To appear in The Asian Journal of Mathematics (AJM) special issue dedicated to Ngaiming Mok's 60th birthda

Comment on "Geometric phases for mixed states during cyclic evolutions"

It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions [2004 {\it J. Phys. A} {\bf 37} 3699] is gauge dependent.Comment: Comment to the paper L.-B. Fu and J.-L. Chen, J. Phys. A 37, 3699 (2004); small changes; journal reference adde

Nonlinear development and secondary instability of Gortler vortices in hypersonic flows

In a hypersonic boundary layer over a wall of variable curvature, the region most susceptible to Goertler vortices is the temperature adjustment layer over which the basic state temperature decreases monotonically to its free stream value. Except for a special wall curvature distribution, the evolution of Goertler vortices trapped in the temperature adjustment layer will in general be strongly affected by the boundary layer growth through the O(M sup 3/2) curvature of the basic state, where M is the free stream Mach number. Only when the local wavenumber becomes as large as of order M sup 3/8, do nonparallel effects become negligible in the determination of stability properties. In the latter case, Goertler vortices will be trapped in a thin layer of O(epsilon sup 1/2) thickness which is embedded in the temperature adjustment layer; here epsilon is the inverse of the local wavenumber. A weakly nonlinear theory is presented in which the initial nonlinear development of Goertler vortices in the neighborhood of the neutral position is studied and two coupled evolution equations are derived. From these, it can be determined whether the vortices are decaying or growing depending on the sign of a constant which is related to wall curvature and the basic state temperature

Chiral Corrections to Hyperon Axial Form Factors

We study the complete set of flavor changing hyperon axial current matrix elements at small momentum transfer. Using partially quenched heavy baryon chiral perturbation theory, we derive the chiral and momentum behavior of the axial and induced pseudoscalar form factors. The meson pole contributions to the latter posses a striking signal for chiral physics. We argue that the study of hyperon axial matrix elements enables a systematic lattice investigation of the efficacy of three flavor chiral expansions in the baryon sector. This can be achieved by considering chiral corrections to SU(3) symmetry predictions, and their partially quenched generalizations. In particular, despite the presence of eight unknown low-energy constants, we are able to make next-to-leading order symmetry breaking predictions for two linear combinations of axial charges.Comment: 23 pages, 3 figures, typos corrected and a new NLO prediction adde

Collapse of electrons to a donor cluster in SrTiO3_3

It is known that a nucleus with charge $Ze$ where $Z>170$ creates electron-positron pairs from the vacuum. These electrons collapse onto the nucleus resulting in a net charge $Z_n<Z$ while the positrons are emitted. This effect is due to the relativistic dispersion law. The same reason leads to the collapse of electrons to the charged impurity with a large charge number $Z$ in narrow-band gap semiconductors and Weyl semimetals as well as graphene. In this paper, a similar effect of electron collapse and charge renormalization is found for donor clusters in SrTiO$_3$ (STO), but with a very different origin. At low temperatures, STO has an enormously large dielectric constant. Because of this, the nonlinear dielectric response becomes dominant when the electric field is not too small. We show that this leads to the collapse of surrounding electrons into a charged spherical donor cluster with radius $R$ when its total charge number $Z$ exceeds a critical value $Z_c\simeq R/a$ where $a$ is the lattice constant. Using the Thomas-Fermi approach, we find that the net charge $Z_ne$ grows with $Z$ until $Z$ exceeds another value $Z^*\simeq(R/a)^{9/7}$. After this point, $Z_n$ remains $\sim Z^*$. We extend our results to the case of long cylindrical clusters. Our predictions can be tested by creating discs and stripes of charge on the STO surface