Bulk and Edge excitations in a ν=1\nu =1 quantum Hall ferromagnet

In this article, we shall focus on the collective dynamics of the fermions in a $\nu = 1$ quantum Hall droplet. Specifically, we propose to look at the quantum Hall ferromagnet. In this system, the electron spins are ordered in the ground state due to the exchange part of the Coulomb interaction and the Pauli exclusion principle. The low energy excitations are ferromagnetic magnons. To provide a means for describing these magnons, we shall discuss a method of introducing collective coordinates in the Hilbert space of many-fermion systems. These collective coordinates are bosonic in nature. They map a part of the fermionic Hilbert space into a bosonic Hilbert space. Using this technique, we shall interpret the magnons as bosonic collective ex citations in the Hilbert space of the many-electron Hall system. By considering a Hall droplet of finite extent, we shall also obtain the effective Lagrangian governing the spin collective excitations at the edge of the sample.Comment: Plain TeX 18 Pages Proceedings for the Y2K conference on strongly c orrelated fermionic systems, Calcutta, Indi

On the giant magnon and spike solutions for strings on AdS3×_3\times S3^3

We study solutions for the rotating strings on the sphere with a background NS-NS field and on the Anti-de-Sitter spacetime. We show the existence of magnon and single spike solutions on R$\times$S$^2$ in the presence of constant magnetic field as two limiting cases. We also study the solution for strings on AdS$_3\times$ S$^3$ with Melvin deformation. The dispersion relations among various conserved charges are shown to receive finite corrections due to the deformation parameter. We further study the rotating string on AdS$_3 \times$ S$^3$ geometry with two conserved angular momenta on S$^3$ and one spin along the AdS$_3$. We show that there exists two kinds of solutions: a circular string solution and a helical string. We find out the dispersion relation among various charges and give physical interpretation of these solutions.Comment: 18 pages, 1 figure, typos fixed, minor changes, to appear in JHE

Phenol degradation using 20, 300 and 520 kHz ultrasonic reactors with hydrogen peroxide, ozone and zero valent metals

The extent of phenol degradation by the advanced oxidation process in the presence of zero valent iron (ZVI) and zero valent copper (ZVC) was studied using 20, 300 and 520 kHz ultrasonic (US) reactors. Quantification of hydrogen peroxide has also been performed with an aim of investigating the efficacy of different sonochemical reactors for hydroxyl radical production. It has been observed that the 300 kHz sonochemical reactor has the maximum efficacy for hydroxyl radical production. Phenol degradation studies clearly indicate that degradation of phenol is intensified in the presence of the catalyst and hydrogen peroxide, which can be attributed to enhanced production of hydroxyl radicals in the system. Experimental data shows that with ZVI, when the reaction was subjected to 300 kHz, complete phenol removal and 37% TOC mineralization was achieved within 25 min, whereas, in the case of 20 kHz US treatment no phenol was detected after 45 min and 39% TOC mineralization was observed. This novel study also investigated the use of zero valent copper (ZVC) and results showed that with 20, 300 and 520 kHz ultrasonic rectors, phenol removal was 10–98%, however, the maximum TOC mineralization achieved was only 26%. A comparative study between hydrogen peroxide and ozone as a suitable oxidant for Fenton-like reactions in conjunction with zero valent catalysts showed that an integrated approach of US/Air/ZVC/H2O2 system works better than US/ZVC/O3 (the ZOO process)