The effects of KSEA interaction on the ground-state properties of spin chains in a transverse field

The effects of symmetric helical interaction which is called the Kaplan, Shekhtman, Entin-Wohlman, and Aharony (KSEA) interaction on the ground-state properties of three kinds of spin chains in a transverse field have been studied by means of correlation functions and chiral order parameter. We find that the anisotropic transition of $XY$ chain in a transverse field ($XY$TF) disappears because of the KSEA interaction. For the other two chains, we find that the regions of gapless chiral phases in the parameter space induced by the DM or $XZY-YZX$ type of three-site interaction are decreased gradually with increase of the strength of KSEA interaction. When it is larger than the coefficient of DM or $XZY-YZX$ type of three-site interaction, the gapless chiral phases also disappear.Comment: 7 pages, 3 figure

Public-private partnerships in China's urban water sector

During the past decades, the traditional state monopoly in urban water management has been debated heavily, resulting in different forms and degrees of private sector involvement across the globe. Since the 1990s, China has also started experiments with new modes of urban water service management and governance in which the private sector is involved. It is premature to conclude whether the various forms of private sector involvement will successfully overcome the major problems (capital shortage, inefficient operation, and service quality) in China¿s water sector. But at the same time, private sector involvement in water provisioning and waste water treatments seems to have become mainstream in transitional China

Volume integrals associated with the inhomegeneous Helmholtz equation. Part 2: Cylindrical region; rectangular region

Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) + alpha(2), for the cases of a finite cylindrical region and a region of rectangular parallelepiped. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r r' and r 4', where r and r' are distances from the origin to the point of observation and source, respectively. When the wave number approaches zero, the results reduce directly to the potentials of variable densities

U(1)U(1) gauge vector field on a codimension-2 brane

In this paper, we obtain a gauge invariant effective action for a bulk massless $U(1)$ gauge vector field on a brane with codimension two by using a general Kaluza-Klein (KK) decomposition for the field. It suggests that there exist two types of scalar KK modes to keep the gauge invariance of the action for the massive vector KK modes. Both the vector and scalar KK modes can be massive. The masses of the vector KK modes $m^{(n)}$ contain two parts, $m_{1}^{(n)}$ and $m_{2}^{(n)}$, due to the existence of the two extra dimensions. The masses of the two types of scalar KK modes $m_{\phi}^{(n)}$ and $m_{\varphi}^{(n)}$ are related to the vector ones, i.e., $m_{\phi}^{(n)}=m_{1}^{(n)}$ and $m_{\varphi}^{(n)}=m_{2}^{(n)}$. Moreover, we derive two Schr\"{o}dinger-like equations for the vector KK modes, for which the effective potentials are just the functions of the warp factor.Comment: 15 pages,no figures, accepted by JHE