Notes on two-parameter quantum groups, (I)

A simpler definition for a class of two-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An operator realization of the positive part is given.Comment: 11 page

Notes on two-parameter quantum groups, (II)

This paper is the sequel to [HP1] to study the deformed structures and representations of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ associated to the finite dimensional simple Lie algebras \mg. An equivalence of the braided tensor categories \O^{r,s} and \O^{q} is explicitly established.Comment: 21 page

The Universal Edge Physics in Fractional Quantum Hall Liquids

The chiral Luttinger liquid theory for fractional quantum Hall edge transport predicts universal power-law behavior in the current-voltage ($I$-$V$) characteristics for electrons tunneling into the edge. However, it has not been unambiguously observed in experiments in two-dimensional electron gases based on GaAs/GaAlAs heterostructures or quantum wells. One plausible cause is the fractional quantum Hall edge reconstruction, which introduces non-chiral edge modes. The coupling between counterpropagating edge modes can modify the exponent of the $I$-$V$ characteristics. By comparing the $\nu=1/3$ fractional quantum Hall states in modulation-doped semiconductor devices and in graphene devices, we show that the graphene-based systems have an experimental accessible parameter region to avoid the edge reconstruction, which is suitable for the exploration of the universal edge tunneling exponent predicted by the chiral Luttinger liquid theory.Comment: 7 pages, 6 figure

The Damping Tail of CMB Anisotropies

By decomposing the damping tail of CMB anisotropies into a series of transfer functions representing individual physical effects, we provide ingredients that will aid in the reconstruction of the cosmological model from small-scale CMB anisotropy data. We accurately calibrate the model-independent effects of diffusion and reionization damping which provide potentially the most robust information on the background cosmology. Removing these effects, we uncover model-dependent processes such as the acoustic peak modulation and gravitational enhancement that can help distinguish between alternate models of structure formation and provide windows into the evolution of fluctuations at various stages in their growth.Comment: 24pgs, aaspp4, 10 figs. included; supporting material (e.g. color figures) at http://www.sns.ias.edu/~whu/pub.htm

Multiple phase transitions in single-crystalline Na1−δ_{1-\delta}FeAs

Specific heat, resistivity, susceptibility and Hall coefficient measurements were performed on high-quality single crystalline Na$_{1-\delta}$FeAs. This compound is found to undergo three successive phase transitions at around 52, 41, and 23 K, which correspond to structural, magnetic and superconducting transitions, respectively. The Hall effect result indicates the development of energy gap at low temperature due to the occurrence of spin-density-wave instability. Our results provide direct experimental evidence of the magnetic ordering in the nearly stoichiometric NaFeAs.Comment: 4 pages, 4 figure

q-Deformation of W(2,2) Lie algebra associated with quantum groups

An explicit realization of the W(2,2) Lie algebra is presented using the famous bosonic and fermionic oscillators in physics, which is then used to construct the q-deformation of this Lie algebra. Furthermore, the quantum group structures on the q-deformation of this Lie algebra are completely determined.Comment: 12 page

Metamagnetic Transition in Na0.85_{0.85}CoO2_2 Single Crystals

We report the magnetization, specific heat and transport measurements of high quality Na$_{0.85}$CoO$_2$ single crystals in applied magnetic fields up to 14T. In high temperatures, the system is in a paramagnetic phase. It undergoes a magnetic phase transition below about 20K. When the field is applied along the c-axis, the measurement data of magnetization, specific heat and magnetoresistance reveal a metamagnetic transition from an antiferromagnetic state to a quasi-ferromagnetic state at about 8T in low temperatures. However, no transition is observed in the magnetization measurements up to 14T when the field is applied perpendicular to the c-axis. The low temperature magnetic phase diagram of Na$_{0.85}$CoO$_2$ is determined.Comment: 4 pages, 5 figure

Angular-dependent Magnetoresistance Oscillations in Na0.48_{0.48}CoO2_{2} Single Crystal

We report measurements of the c-axis angular-dependent magnetoresistance (AMR) for a Na$_{0.48}$CoO$_{2}$ single crystal, with a magnetic field of 10 T rotating within Co-O planes. Below the metal-insulator transition temperature induced by the charge ordering, the oscillation of the AMR is dominated by a two-fold rotational symmetry. The amplitudes of the oscillation corresponding to the four- and six-fold rotational symmetries are distinctive in low temperatures, but they merge into the background simultaneously at about 25 K. The six-fold oscillation originates naturally from the lattice symmetry. The observation of the four-fold rotational symmetry is consistent with the picture proposed by Choy, et al., that the Co lattice in the charge ordered state will split into two orthorhombic sublattice with one occupied by Co$^{3+}$ ions and the other by Co$^{4+}$ ions. We have also measured the c-axis AMR for Na$_{0.35}$CoO$_{2}$ and Na$_{0.85}$CoO$_{2}$ single crystals, and found no evidence for the existence of two- and four-fold symmetries.Comment: 4 pages, 6 figures. Submitted to PR