Field Theoretical Description of Quantum Hall Edge Reconstruction

We propose a generalization of the chiral Luttinger liquid theory to allow for a unified description of quantum Hall edges with or without edge reconstruction. Within this description edge reconstruction is found to be a quantum phase transition in the universality class of one-dimensional dilute Bose gas transition, whose critical behavior can be obtained exactly. At principal filling factors $\nu=1/m$, we show the additional edge modes due to edge reconstruction modifies the point contact tunneling exponent in the low energy limit, by a small and non-universal amount.Comment: 4 pages with 1 ps figure embedde

Dynamical state of galaxy clusters evaluated from X-ray images

X-ray images of galaxy clusters often show disturbed structures that are indication of cluster mergers. As a complementary to our previous work on dynamical state of 964 clusters observed by the Chandra, we process the X-ray images for 1308 clusters from XMM-Newton archival data, together with the images of 22 clusters newly released by the Chandra, and evaluate their dynamical state from these X-ray images. The concentration index $c$, the centroid shift $\omega$, the power ratio $P_3/P_0$ are calculated in circular regions with a certain radius of 500 kpc, and the morphology index $\delta$ is estimated within elliptical regions adaptive to the cluster size and shape. In addition, the dynamical parameters for 42 clusters previously estimated from Chandra images are upgraded based on the newly available redshifts. Good consistence is found between dynamical parameters derived from XMM-Newton and Chandra images for the overlapped sample of clusters in the two datasets. The dependence of mass scaling relations on dynamical state is shown by using data of 388 clusters.Comment: 10 pages, 6 figures, 4 tables, MNRAS in pres

How universal is the fractional-quantum-Hall edge Luttinger liquid?

This article reports on our microscopic investigations of the edge of the fractional quantum Hall state at filling factor $\nu=1/3$. We show that the interaction dependence of the wave function is well described in an approximation that includes mixing with higher composite-fermion Landau levels in the lowest order. We then proceed to calculate the equal time edge Green function, which provides evidence that the Luttinger exponent characterizing the decay of the Green function at long distances is interaction dependent. The relevance of this result to tunneling experiments is discussed.Comment: 5 page

Relevance of inter-composite fermion interaction to the edge Tomonaga-Luttinger liquid

It is shown that Wen's effective theory correctly describes the Tomonaga-Luttinger liquid at the edge of a system of non-interacting composite fermions. However, the weak residual interaction between composite fermions appears to be a relevant perturbation. The filling factor dependence of the Tomonaga-Luttinger parameter is estimated for interacting composite fermions in a microscopic approach and satisfactory agreement with experiment is achieved. It is suggested that the electron field operator may not have a simple representation in the effective one dimensional theory.Comment: 5 pages; accepted in Phys. Rev. Let