Measures of entanglement in multipartite bound entangled states

Bound entangled states are states that are entangled but from which no entanglement can be distilled if all parties are allowed only local operations and classical communication. However, in creating these states one needs nonzero entanglement resources to start with. Here, the entanglement of two distinct multipartite bound entangled states is determined analytically in terms of a geometric measure of entanglement and a related quantity. The results are compared with those for the negativity and the relative entropy of entanglement.Comment: 5 pages, no figure; title change

k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions

We show that hard-scattering factorization is violated in the production of high-p_T hadrons in hadron-hadron collisions, in the case that the hadrons are back-to-back, so that k_T factorization is to be used. The explicit counterexample that we construct is for the single-spin asymmetry with one beam transversely polarized. The Sivers function needed here has particular sensitivity to the Wilson lines in the parton densities. We use a greatly simplified model theory to make the breakdown of factorization easy to check explicitly. But the counterexample implies that standard arguments for factorization fail not just for the single-spin asymmetry but for the unpolarized cross section for back-to-back hadron production in QCD in hadron-hadron collisions. This is unlike corresponding cases in e^+e^- annihilation, Drell-Yan, and deeply inelastic scattering. Moreover, the result endangers factorization for more general hadroproduction processes.Comment: 10 pages. V. 2: Title change, misprints and minor corrections, as in journal versio

Low-energy electronic recoil in xenon detectors by solar neutrinos

Low-energy electronic recoil caused by solar neutrinos in multi-ton xenon detectors is an important subject not only because it is a source of the irreducible background for direct searches of weakly-interacting massive particles (WIMPs), but also because it provides a viable way to measure the solar $pp$ and $^{7}\textrm{Be}$ neutrinos at the precision level of current standard solar model predictions. In this work we perform $\textit{ab initio}$ many-body calculations for the structure, photoionization, and neutrino-ionization of xenon. It is found that the atomic binding effect yields a sizable suppression to the neutrino-electron scattering cross section at low recoil energies. Compared with the previous calculation based on the free electron picture, our calculated event rate of electronic recoil in the same detector configuration is reduced by about $25\%$. We present in this paper the electronic recoil rate spectrum in the energy window of 100 eV - 30 keV with the standard per ton per year normalization for xenon detectors, and discuss its implication for low energy solar neutrino detection (as the signal) and WIMP search (as a source of background).Comment: 12 pages, 3 figure

A dynamical approximation for stochastic partial differential equations

Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the random invariant manifold is almost surely asymptotically complete. The asymptotic dynamical behavior is thus described by a stochastic ordinary differential system on the random invariant manifold, under suitable conditions. As an application, stationary states (invariant measures) is considered for one example of stochastic partial differential equations.Comment: 28 pages, no figure