About J-flow, J-balanced metrics, uniform J-stability and K-stability

From the work of Dervan-Keller, there exists a quantization of the critical equation for the J-flow. This leads to the notion of J-balanced metrics. We prove that the existence of J-balanced metrics has a purely algebro-geometric characterization in terms of Chow stability, complementing the result of Dervan-Keller. We also obtain various criteria that imply uniform J-stability and uniform K-stability. Eventually, we discuss the case of K\"ahler classes that may not be integral over a compact manifold.Comment: 23 pages; In honor of Ngaiming Mok's 60th birthday. To appear in Asian J. Mat

Isotropic realizability of current fields in R^3

This paper deals with the isotropic realizability of a given regular divergence free field j in R^3 as a current field, namely to know when j can be written as sigma Du for some isotropic conductivity sigma, and some gradient field Du. The local isotropic realizability in R^3 is obtained by Frobenius' theorem provided that j and curl j are orthogonal in R^3. A counter-example shows that Frobenius' condition is not sufficient to derive the global isotropic realizability in R^3. However, assuming that (j, curl j, j x curl j) is an orthogonal basis of R^3, an admissible conductivity sigma is constructed from a combination of the three dynamical flows along the directions j/|j|, curl j/|curl j| and (j/|j|^2) x curl j. When the field j is periodic, the isotropic realizability in the torus needs in addition a boundedness assumption satisfied by the flow along the third direction (j/|j|^2) x \curl j. Several examples illustrate the sharpness of the realizability conditions.Comment: 22 page

Systematic analysis of the DJ(2580)D_{J}(2580), DJ∗(2650)D_{J}^{*}(2650), DJ(2740)D_{J}(2740), DJ∗(2760)D_{J}^{*}(2760), DJ(3000)D_{J}(3000) and DJ∗(3000)D_{J}^{*}(3000) in DD meson family

In this work, we tentatively assign the charmed mesons $D_{J}(2580)$, $D_{J}^{*}(2650)$, $D_{J}(2740)$, $D_{J}^{*}(2760)$, $D_{J}(3000)$ and $D_{J}^{*}(3000)$ observed by the LHCb collaboration according to their spin-parity and masses, then study their strong decays to the ground state charmed mesons plus light pseudoscalar mesons with the $^{3}P_{0}$ model. According to these study, we assigned the $D_{J}^{*}(2760)$ as the $1D\frac{5}{2}3^{-}$ state, the $D_{J}^{*}(3000)$ as the $1F\frac{5}{2}2^{+}$ or $1F\frac{7}{2}4^{+}$ state, the $D_{J}(3000)$ as the $1F\frac{7}{2}3^{+}$ or $2P\frac{1}{2}1^{+}$ state in the $D$ meson family. As a byproduct, we also study the strong decays of $2P\frac{1}{2}0^{+}$,$2P\frac{3}{2}2^{+}$, $3S\frac{1}{2}1^{-}$, $3S\frac{1}{2}0^{-}$ etc, states, which will be helpful to further experimentally study mixings of these $D$ mesons.Comment: 16 pages,1 figure. arXiv admin note: text overlap with arXiv:0801.4821 by other author

Impurity Energy Level Within The Haldane Gap

An impurity bond $J{'}$ in a periodic 1D antiferromagnetic, spin 1 chain with exchange $J$ is considered. Using the numerical density matrix renormalization group method, we find an impurity energy level in the Haldane gap, corresponding to a bound state near the impurity bond. When $J{'}<J$ the level changes gradually from the edge of the Haldane gap to the ground state energy as the deviation $dev=(J-J{'})/J$ changes from 0 to 1. It seems that there is no threshold. Yet, there is a threshold when $J{'}>J$. The impurity level appears only when the deviation $dev=(J{'}-J)/J{'}$ is greater than $B_{c}$, which is near 0.3 in our calculation.Comment: Latex file,9 pages uuencoded compressed postscript including 4 figure