Transport of Surface States in the Bulk Quantum Hall Effect

The two-dimensional surface of a coupled multilayer integer quantum Hall system consists of an anisotropic chiral metal. This unusual metal is characterized by ballistic motion transverse and diffusive motion parallel (\hat{z}) to the magnetic field. Employing a network model, we calculate numerically the phase coherent two-terminal z-axis conductance and its mesoscopic fluctuations. Quasi-1d localization effects are evident in the limit of many layers. We consider the role of inelastic de-phasing effects in modifying the transport of the chiral surface sheath, discussing their importance in the recent experiments of Druist et al.Comment: 9 pages LaTex, 9 postscript figures included using eps

Feynman's Propagator Applied to Network Models of Localization

Network models of dirty electronic systems are mapped onto an interacting field theory of lower dimensionality by intepreting one space dimension as time. This is accomplished via Feynman's interpretation of anti-particles as particles moving backwards in time. The method developed maps calculation of the moments of the Landauer conductance onto calculation of correlation functions of an interacting field theory of bosons and fermions. The resulting field theories are supersymmetric and closely related to the supersymmetric spin-chain representations of network models recently discussed by various authors. As an application of the method, the two-edge Chalker-Coddington model is shown to be Anderson localized, and a delocalization transition in a related two-edge network model (recently discussed by Balents and Fisher) is studied by calculation of the average Landauer conductance.Comment: Latex, 14 pages, 2 fig

Blowup Criterion for the Compressible Flows with Vacuum States

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional compressible Navier-Stokes equations, which will happen, for example, if the initial density is compactly supported \cite{X1}. More precisely, if a solution of the compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce's criterion for 3-dimensional incompressible Euler equations (\cite{po}). Moreover, our method can be generalized to the full Compressible Navier-Stokes system which improve the previous results. In addition, initial vacuum states are allowed in our cases.Comment: 17 page

Blow up criterion for compressible nematic liquid crystal flows in dimension three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of gradient of liquid crystal director field.Comment: 22 page

Quasinormal modes for tensor and vector type perturbation of Gauss Bonnet black holes using third order WKB approach

We obtain the quasinormal modes for tensor perturbations of Gauss-Bonnet (GB) black holes in $d=5, 7, 8$ dimensions and vector perturbations in $d = 5, 6, 7$ and 8 dimensions using third order WKB formalism. The tensor perturbation for black holes in $d=6$ is not considered because of the fact that it is unstable to tensor mode perturbations. In the case of uncharged GB black hole, for both tensor and vector perturbations, the real part of the QN frequency increases as the Gauss-Bonnet coupling ($\alpha'$) increases. The imaginary part first decreases upto a certain value of $\alpha'$ and then increases with $\alpha'$ for both tensor and vector perturbations. For larger values of $\alpha'$, the QN frequencies for vector perturbation differs slightly from the QN frequencies for tensorial one. It has also been shown that as $\alpha' \to 0$, the quasinormal mode frequency for tensor and vector perturbation of the Schwarzschild black hole can be obtained. We have also calculated the quasinormal spectrum of the charged GB black hole for tensor perturbations. Here we have found that the real oscillation frequency increases, while the imaginary part of the frequency falls with the increase of the charge. We also show that the quasinormal frequencies for scalar field perturbations and the tensor gravitational perturbations do not match as was claimed in the literature. The difference in the result increases if we increase the GB coupling.Comment: 17 pages, 11 figures, change in title and abstract, new equations and results added for QN frequencies for vector perturbations, new referencees adde

Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states

When the two-dimensional random-bond Ising model is represented as a noninteracting fermion problem, it has the same symmetries as an ensemble of random matrices known as class D. A nonlinear sigma model analysis of the latter in two dimensions has previously led to the prediction of a metallic phase, in which the fermion eigenstates at zero energy are extended. In this paper we argue that such behavior cannot occur in the random-bond Ising model, by showing that the Ising spin correlations in the metallic phase violate the bound on such correlations that results from the reality of the Ising couplings. Some types of disorder in spinless or spin-polarized p-wave superconductors and paired fractional quantum Hall states allow a mapping onto an Ising model with real but correlated bonds, and hence a metallic phase is not possible there either. It is further argued that vortex disorder, which is generic in the fractional quantum Hall applications, destroys the ordered or weak-pairing phase, in which nonabelian statistics is obtained in the pure case.Comment: 13 pages; largely independent of cond-mat/0007254; V. 2: as publishe

Short-Range Interactions and Scaling Near Integer Quantum Hall Transitions

We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which represents the transition in the non-interacting system. We find, nevertheless, that transport properties change discontinuously when interactions are introduced. Most importantly, in the thermodynamic limit the conductivity at finite temperature is zero without interactions, but non-zero in the presence of arbitrarily weak interactions. In addition, scaling as a function of frequency, $\omega$, and temperature, $T$, is determined by the scaling variable $\omega/T^p$ (where $p$ is the exponent for the temperature dependence of the inelastic scattering rate) and not by $\omega/T$, as it would be at a conventional quantum phase transition described by an interacting fixed point. We express the inelastic exponent, $p$, and the thermal exponent, $z_T$, in terms of the scaling dimension, $-\alpha < 0$, of the interaction strength and the dynamical exponent $z$ (which has the value $z=2$), obtaining $p=1+2\alpha/z$ and $z_T=2/p$.Comment: 9 pages, 4 figures, submitted to Physical Review

Generalised Israel Junction Conditions for a Gauss-Bonnet Brane World

In spacetimes of dimension greater than four it is natural to consider higher order (in R) corrections to the Einstein equations. In this letter generalized Israel junction conditions for a membrane in such a theory are derived. This is achieved by generalising the Gibbons-Hawking boundary term. The junction conditions are applied to simple brane world models, and are compared to the many contradictory results in the literature.Comment: 4 page

Gauss-Bonnet Black Holes in dS Spaces

We study the thermodynamic properties associated with black hole horizon and cosmological horizon for the Gauss-Bonnet solution in de Sitter space. When the Gauss-Bonnet coefficient is positive, a locally stable small black hole appears in the case of spacetime dimension $d=5$, the stable small black hole disappears and the Gauss-Bonnet black hole is always unstable quantum mechanically when $d \ge 6$. On the other hand, the cosmological horizon is found always locally stable independent of the spacetime dimension. But the solution is not globally preferred, instead the pure de Sitter space is globally preferred. When the Gauss-Bonnet coefficient is negative, there is a constraint on the value of the coefficient, beyond which the gravity theory is not well defined. As a result, there is not only an upper bound on the size of black hole horizon radius at which the black hole horizon and cosmological horizon coincide with each other, but also a lower bound depending on the Gauss-Bonnet coefficient and spacetime dimension. Within the physical phase space, the black hole horizon is always thermodynamically unstable and the cosmological horizon is always stable, further, as the case of the positive coefficient, the pure de Sitter space is still globally preferred. This result is consistent with the argument that the pure de Sitter space corresponds to an UV fixed point of dual field theory.Comment: Rextex, 17 pages including 8 eps figures, v2: minor changes, to appear in PRD, v3: references adde

Slowly rotating charged black holes in anti-de Sitter third order Lovelock gravity

In this paper, we study slowly rotating black hole solutions in Lovelock gravity (n=3). These exact slowly rotating black hole solutions are obtained in uncharged and charged cases, respectively. Up to the linear order of the rotating parameter a, the mass, Hawking temperature and entropy of the uncharged black holes get no corrections from rotation. In charged case, we compute magnetic dipole moment and gyromagnetic ratio of the black holes. It is shown that the gyromagnetic ratio keeps invariant after introducing the Gauss-Bonnet and third order Lovelock interactions.Comment: 14 pages, no figur