Toward a Conformal Field Theory for the Quantum Hall Effect

An effective Hamiltonian for the study of the quantum Hall effect is proposed. This Hamiltonian, which includes a ``current-current" interaction has the form of a Hamiltonian for a conformal field theory in the large $N$ limit. An order parameter is constructed from which the Hamiltonian may be derived. This order parameter may be viewed as either a collective coordinate for a system of $N$ charged particles in a strong magnetic field; or as a field of spins associated with the cyclotron motion of these particles.Comment: 14 pg

Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges

For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory, the general parameter dependent distribution between two sets of eigenvalues with two different parameter values can be expressed as a quaternion determinant. For the parameter dependent Gaussian and Laguerre ensembles the matrix elements of the determinant are expressed in terms of corresponding skew-orthogonal polynomials, and their limiting value for infinite matrix dimension are computed in the vicinity of the soft and hard edges respectively. A connection formula relating the distributions at the hard and soft edge is obtained, and a universal asymptotic behaviour of the two point correlation is identified.Comment: 37 pgs., 1fi

Spectral Density of Complex Networks with a Finite Mean Degree

In order to clarify the statistical features of complex networks, the spectral density of adjacency matrices has often been investigated. Adopting a static model introduced by Goh, Kahng and Kim, we analyse the spectral density of complex scale free networks. For that purpose, we utilize the replica method and effective medium approximation (EMA) in statistical mechanics. As a result, we identify a new integral equation which determines the asymptotic spectral density of scale free networks with a finite mean degree $p$. In the limit $p \to \infty$, known asymptotic formulae are rederived. Moreover, the $1/p$ corrections to known results are analytically calculated by a perturbative method.Comment: 18 pages, 1 figure, minor corrections mad

Determiningeons : a computer program for approximating lie generators admitted by dynamical systems

As was recognized by same of the most reputable physicists of the world such as Galilee and Einstein, the basic laws of physics must inevitably be founded upon invariance principles. Galilean and special relativity stand as historical landmarks that emphasize this message. It\u27s no wonder that the great developments of modern physics (such as those in elementary particle physics) have been keyed upon this concept. The modern formulation of classical mechanics (see Abraham and Marsden [1]) is based upon qualitative or geometric analysis. This is primarily due to the works of Poincare. Poincare showed the value of such geometric analysis in the solution of otherwise insoluble problems in stability theory. It seems that the insights of Poincare have proven fruitful by the now famous works of Kolmogorov, Arnold, and Moser. The concepts used in this geometric theory are again based upon invariance principles, or symmetries. The work of Sophus Lie from 1873 to 1893 laid the groundwork for the analysis of invariance or symmetry principles in modern physics. His primary studies were those of partial differential equations. This led him to the study of the theory of transformations and inevitably to the analysis of abstract groups and differential geometry. Here we show same further applications of Lie group theory through the use of transformation groups. We emphasize the use of transformation invariance to find conservation laws and dynamical properties in chemical physics

Spectra of massive QCD dirac operators from random matrix theory: All three chiral symmetry breaking patterns

The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low-energy correlation functions of all three chiral symmetry breaking patterns (labeled by the Dyson index β = 1, 2 and 4) on the same footing, offering a unifying description of massive QCD Dirac spectra. RMT universality is explicitly proven for all three symmetry classes and the results are compared to the available lattice data for β = 4

Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition

We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit) this theory is in one to one correspondence to the partition function of Wilson chiral perturbation theory in the epsilon regime, such as the related two matrix-model previously introduced in refs. [20,21]. For a generic number of flavours and rectangular block matrices in the chGUE part we derive an eigenvalue representation for the partition function displaying a Pfaffian structure. In the quenched case with nu=0,1 we derive all spectral correlations functions in our model for finite-n, given in terms of skew-orthogonal polynomials. The latter are expressed as Gaussian integrals over standard Laguerre polynomials. In the weakly non-chiral microscopic limit this yields all corresponding quenched eigenvalue correlation functions of the Hermitian Wilson operator.Comment: 27 pages, 4 figures; v2 typos corrected, published versio

Determinantal process starting from an orthogonal symmetry is a Pfaffian process

When the number of particles $N$ is finite, the noncolliding Brownian motion (BM) and the noncolliding squared Bessel process with index $\nu > -1$ (BESQ$^{(\nu)}$) are determinantal processes for arbitrary fixed initial configurations. In the present paper we prove that, if initial configurations are distributed with orthogonal symmetry, they are Pfaffian processes in the sense that any multitime correlation functions are expressed by Pfaffians. The $2 \times 2$ skew-symmetric matrix-valued correlation kernels of the Pfaffians processes are explicitly obtained by the equivalence between the noncolliding BM and an appropriate dilatation of a time reversal of the temporally inhomogeneous version of noncolliding BM with finite duration in which all particles start from the origin, $N \delta_0$, and by the equivalence between the noncolliding BESQ$^{(\nu)}$ and that of the noncolliding squared generalized meander starting from $N \delta_0$.Comment: v2: AMS-LaTeX, 17 pages, no figure, corrections made for publication in J.Stat.Phy

A retrospective case-control study of hepatitis C virus infection and oral lichen planus in Japan: association study with mutations in the core and NS5A region of hepatitis C virus

<p>Abstract</p> <p>Background</p> <p>The aims of this study were to assess the prevalence of hepatitis C virus (HCV) infection in Japanese patients with oral lichen planus and identify the impact of amino acid (aa) substitutions in the HCV core region and IFN-sensitivity-determining region (ISDR) of nonstructural protein 5A (NS5A) associated with lichen planus.</p> <p>Methods</p> <p>In this retrospective study, 59 patients (group 1-A) with oral lichen planus among 226 consecutive patients who visited our hospital and 85 individuals (group 1-B, controls) with normal oral mucosa were investigated for the presence of liver disease and HCV infection. Risk factors for the presence of oral lichen planus were assessed by logistic regression analysis. We compared aa substitutions in the HCV core region (70 and/or 91) and ISDR of NS5A of 12 patients with oral lichen planus (group 2-A) and 7 patients who did not have oral lichen planus (group 2-B) among patients (high viral loads, genotype 1b) who received interferon (IFN) therapy in group1-A.</p> <p>Results</p> <p>The prevalence of anti-HCV and HCV RNA was 67.80% (40/59) and 59.32% (35/59), respectively, in group 1-A and 31.76% (27/85) and 16.47% (14/85), respectively, in group 1-B. The prevalence of anti-HCV (<it>P </it>< 0.0001) and HCV RNA (<it>P </it>< 0.0001) in group 1-A was significantly higher than those in group 1-B. According to multivariate analysis, three factors - positivity for HCV RNA, low albumin level (< 4.0 g/dL), and history of smoking - were associated with the development of oral lichen planus. The adjusted odds ratios for these three factors were 6.58, 3.53 and 2.58, respectively, and each was statistically significant. No significant differences in viral factors, such as aa substitutions in the core region and ISDR of NS5A, were detected between the two groups (groups 2-A and -B).</p> <p>Conclusion</p> <p>We observed a high prevalence of HCV infection in patients with oral lichen planus. Longstanding HCV infection, hypoalbuminemia, and smoking were significant risk factors for the presence of oral lichen planus in patients. It is advisable for Japanese patients with lichen planus to be tested for HCV infection during medical examination.</p