A note on modular forms and generalized anomaly cancellation formulas

By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formula

Korringa ratio of ferromagnetically correlated impure metals

The Korringa ratio, $\cal K$, obtained by taking an appropriate combination of the Knight shift and nuclear spin-lattice relaxation time, is calculated at finite temperature, $T$, in the three-dimensional electron gas model, including the electron-electron interaction, $U$, and non-magnetic impurity scatterings. $\cal K$ varies in a simple way with respect to $U$ and $T$; it decreases as $U$ is increased but increases as $T$ is raised. However, $\cal K$ varies in a slightly more complicated way with respect to the impurity scatterings; as the scattering rate is increased, $\cal K$ increases for small $U$ and low $T$, but decreases for large $U$ or high $T$ regime. This calls for a more careful analysis when one attempts to estimate the Stoner factor from $\cal K$.Comment: 7 pages including 3 figures. To be published in Phys. Rev. B, Dec.

Bounds for state-dependent quantum cloning

Due to the no-cloning theorem, the unknown quantum state can only be cloned approximately or exactly with some probability. There are two types of cloners: universal and state-dependent cloner. The optimal universal cloner has been found and could be viewed as a special state-dependent quantum cloner which has no information about the states. In this paper, we investigate the state-dependent cloning when the state-set contains more than two states. We get some bounds of the global fidelity for these processes. This method is not dependent on the number of the states contained in the state-set. It is also independent of the numbers of copying.Comment: 13 pages, 1 figure, to appear in Phys. Rev.

A general type of twisted anomaly cancellation formulas

For even dimensional manifolds, we prove some twisted anomaly cancellation formulas which generalize some well-known cancellation formulas. For odd dimensional manifolds, we obtain some modularly invariant characteristic forms by the Chern-Simons transgression and we also get some twisted anomaly cancellation formulas