The consequences of SU(3) colorsingletness, Polyakov Loop and Z(3) symmetry on a quark-gluon gas

Based on quantum statistical mechanics we show that the $SU(3)$ color singlet ensemble of a quark-gluon gas exhibits a $Z(3)$ symmetry through the normaized character in fundamental representation and also becomes equivalent, within a stationary point approximation, to the ensemble given by Polyakov Loop. Also Polyakov Loop gauge potential is obtained by considering spatial gluons along with the invariant Haar measure at each space point. The probability of the normalized character in $SU(3)$ vis-a-vis Polyakov Loop is found to be maximum at a particular value exhibiting a strong color correlation. This clearly indicates a transition from a color correlated to uncorrelated phase or vise-versa. When quarks are included to the gauge fields, a metastable state appears in the temperature range $145\le T({\rm{MeV}}) \le 170$ due to the explicit $Z(3)$ symmetry breaking in the quark-gluon system. Beyond $T\ge 170$ MeV the metastable state disappears and stable domains appear. At low temperature a dynamical recombination of ionized $Z(3)$ color charges to a color singlet $Z(3)$ confined phase is evident along with a confining background that originates due to circulation of two virtual spatial gluons but with conjugate $Z(3)$ phases in a closed loop. We also discuss other possible consequences of the center domains in the color deconfined phase at high temperature.Comment: Version published in J. Phys.

Size distribution of sputtered particles from Au nanoislands due to MeV self-ion bombardment

Nanoisland gold films, deposited by vacuum evaporation of gold onto Si(100) substrates, were irradiated with 1.5 MeV Au$^{2+}$ ions up to a fluence of $5\times 10^{14}$ ions cm$^{-2}$ and at incidence angles up to $60^{\circ}$ with respect to the surface normal. The sputtered particles were collected on carbon coated grids (catcher grid) during ion irradiation and were analyzed with transmission electron microscopy and Rutherford backscattering spectrometry. The average sputtered particle size and the areal coverage are determined from transmission electron microscopy measurements, whereas the amount of gold on the substrate is found by Rutherford backscattering spectrometry. The size distributions of larger particles (number of atoms/particle, $n$ $\ge$ 1,000) show an inverse power-law with an exponent of $\sim$ -1 in broad agreement with a molecular dynamics simulation of ion impact on cluster targets.Comment: 13 pages, 8 figures, Submitted for publication in JA

Four Zero Texture Fermion Mass Matrices in SO(10) GUT

We attempt the integration of the phenomenologically successful four zero texture of fermion mass matrices with the renormalizable SO(10) GUT. The resulting scenario is found to be highly predictive. Firstly, we examine the phenomenological implications of a class of the lepton mass matrices with parallel texture structures and obtain interesting constraints on the parameters of the charged lepton and the neutrino mass matrices. We combine these phenomenological constraints with the constraints obtained from SO(10) GUT to reduce the number of the free parameters and to further constrain the allowed ranges of the free parameters. The solar/atmospheric mixing angles obtained in this analysis are in fairly good agreement with the data.Comment: 14 pages, 3 figures, 1 tabl

Band Structure of the Fractional Quantum Hall Effect

The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides an accurate and complete microscopic description of the strongly correlated many-body states in the low-energy bands. Thus, somewhat like in Landau's fermi liquid theory, there is a one-to-one correspondence between the low energy Hilbert space of strongly interacting electrons in the fractinal quantum Hall regime and that of weakly interacting electrons in the integer quantum Hall regime.Comment: 10 page

Replicating Nanostructures on Silicon by Low Energy Ion Beams

We report on a nanoscale patterning method on Si substrates using self-assembled metal islands and low-energy ion-beam irradiation. The Si nanostructures produced on the Si substrate have a one-to-one correspondence with the self-assembled metal (Ag, Au, Pt) nanoislands initially grown on the substrate. The surface morphology and the structure of the irradiated surface were studied by high-resolution transmission electron microscopy (HRTEM). TEM images of ion-beam irradiated samples show the formation of sawtooth-like structures on Si. Removing metal islands and the ion-beam induced amorphous Si by etching, we obtain a crystalline nanostructure of Si. The smallest structures emit red light when exposed to a UV light. The size of the nanostructures on Si is governed by the size of the self-assembled metal nanoparticles grown on the substrate for this replica nanopatterning. The method can easily be extended for tuning the size of the Si nanostructures by the proper choice of the metal nanoparticles and the ion energy in ion-irradiation. It is suggested that off-normal irradiation can also be used for tuning the size of the nanostructures.Comment: 12 pages, 7 figures, regular paper submitted to Nanotechnolog

School-based Understanding of Human Rights in Four Countries: A Commonwealth Study

Teaching/Communication/Extension/Profession,