On spectra and Brown's spectral measures of elements in free products of matrix algebras

We compute spectra and Brown measures of some non self-adjoint operators in (M_2(\cc), {1/2}Tr)*(M_2(\cc), {1/2}Tr), the reduced free product von Neumann algebra of M_2(\cc) with M_2(\cc). Examples include $AB$ and $A+B$, where A and B are matrices in (M_2(\cc), {1/2}Tr)*1 and 1*(M_2(\cc), {1/2}Tr), respectively. We prove that AB is an R-diagonal operator (in the sense of Nica and Speicher \cite{N-S1}) if and only if Tr(A)=Tr(B)=0. We show that if X=AB or X=A+B and A,B are not scalar matrices, then the Brown measure of X is not concentrated on a single point. By a theorem of Haagerup and Schultz \cite{H-S1}, we obtain that if X=AB or X=A+B and $X\neq \lambda 1$, then X has a nontrivial hyperinvariant subspace affiliated with (M_2(\cc), {1/2}Tr)*(M_2(\cc), {1/2}Tr).Comment: final version. to appear on Math. Sca

Effect of sea quarks on single-spin asymmetries ANW±A^{W^{\pm}}_{N} in transversely polarized pp collisions at RHIC

We calculate the single-spin asymmetries $A^{W^{\pm}}_{N}$ of $W^{\pm}$ bosons produced in transversely polarized pp collisions with the valence part of the up (u) and down (d) quark Sivers functions treated by an available parametrization and the light-cone quark spectator-diquark model respectively, while the sea part Sivers functions of u and d quarks treated as parametrization. Comparing our results with those from experimental data at RHIC, we find that the Sivers functions of sea quarks play an important role in the determination of the shapes of $A^{W^{\pm}}_{N}$. It is shown that $A^{W^{-}}_{N}$ is sensitive to u sea Sivers function, while $A^{W^{+}}_{N}$ to d sea Sivers function intuitively. The results show that the contributions of u and d sea Sivers functions are rather sizable and of the same sign, and their signs agree with that of d valence quarks and are opposite to that of u valence quarks.Comment: 14 latex pages, 6 figures, final published versio

Effect of sea quarks on the single-spin asymmetries ALW±A^{W^{\pm}}_{L} in polarized pp collisions at RHIC

We calculate the single-spin asymmetries $A^{W^{\pm}}_{L}$ of $W^{\pm}$ bosons produced in polarized pp collisions with the valence part of the up and down quark helicity distributions modeled by the light-cone quark-spectator-diquark model while the sea part helicity distributions of the up and down quarks treated as parametrization. Comparing our results with those from experimental data at RHIC, we find that the helicity distributions of sea quarks play an important role in the determination of the shapes of $A^{W^{\pm}}_{L}$. It is shown that $A^{W^{-}}_{L}$ is sensitive to $\Delta \bar u$, while $A^{W^{+}}_{L}$ to $\Delta \bar d$ intuitively. The experimental data of the polarized structure functions and the sum of helicities are also important to constrain the sizes of quark helicity distributions both for the sea part and the valence part of the nucleon.Comment: 19 latex pages, 5 figures, final version for publicatio

Charge redistribution at the antiferromagnetic phase transition in SrFeAsF compound

The relationship between spin, electron, and crystal structure has been one of the foremost issues in understanding the superconducting mechanism since the discovery of iron-based high temperature superconductors. Here, we report M\"ossbauer and first-principles calculations studies of the parent compound SrFeAsF with the largest temperature gap ($\sim$50\,K) between the structural and antiferromagnetic (AFM) transitions. Our results reveal that the structural transition has little effect on the electronic structure of the compound SrFeAsF while the development of the AFM order induces a redistribution of the charges near the Fermi level.Comment: 6 Pages, 7 Figure