The Kagome Antiferromagnet: A Schwinger-Boson Mean-Field Theory Study

The Heisenberg antiferromagnet on the Kagom\'{e} lattice is studied in the framework of Schwinger-boson mean-field theory. Two solutions with different symmetries are presented. One solution gives a conventional quantum state with $\mathbf{q}=0$ order for all spin values. Another gives a gapped spin liquid state for spin $S=1/2$ and a mixed state with both $\mathbf{q}=0$ and $\sqrt{3}\times \sqrt{3}$ orders for spin $S>1/2$. We emphasize that the mixed state exhibits two sets of peaks in the static spin structure factor. And for the case of spin $S=1/2$, the gap value we obtained is consistent with the previous numerical calculations by other means. We also discuss the thermodynamic quantities such as the specific heat and magnetic susceptibility at low temperatures and show that our result is in a good agreement with the Mermin-Wagner theorem.Comment: 9 pages, 5 figure

Multiple G-It\^{o} integral in the G-expectation space

In this paper, motivated by mathematic finance we introduce the multiple G-It\^{o} integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite polynomials and multiple G-It\^{o} integrals which is a natural extension of the classical result obtained by It\^{o} in 1951.Comment: 9 page

Dichotomy in the Dynamical Status of Massive Cores in Orion

To study the evolution of high mass cores, we have searched for evidence of collapse motions in a large sample of starless cores in the Orion molecular cloud. We used the Caltech Submillimeter Observatory telescope to obtain spectra of the optically thin (\H13CO+) and optically thick (\HCO+) high density tracer molecules in 27 cores with masses $>$ 1 \Ms. The red- and blue-asymmetries seen in the line profiles of the optically thick line with respect to the optically thin line indicate that 2/3 of these cores are not static. We detect evidence for infall (inward motions) in 9 cores and outward motions for 10 cores, suggesting a dichotomy in the kinematic state of the non-static cores in this sample. Our results provide an important observational constraint on the fraction of collapsing (inward motions) versus non-collapsing (re-expanding) cores for comparison with model simulations.Comment: 9 pages, 2 Figures. To appear in ApJ(Letters