Orthogonal Polynomials and Exact Correlation Functions for Two Cut Random Matrix Models

Exact eigenvalue correlation functions are computed for large $N$ hermitian one-matrix models with eigenvalues distributed in two symmetric cuts. An asymptotic form for orthogonal polynomials for arbitrary polynomial potentials that support a $Z_2$ symmetric distribution is obtained. This results in an exact explicit expression for the kernel at large $N$ which determines all eigenvalue correlators. The oscillating and smooth parts of the two point correlator are extracted and the universality of local fine grained and smoothed global correlators is established.Comment: 15 pages, LaTex, a paragraph added in note added:, three references added. accepted in Nucl. Phys.

Graphene with wedge disclination in the presence of intrinsic and Rashba spin orbit couplings

In this article, the modified Kane-Mele Hamiltonian is derived for graphene with wedge disclination and spin orbit couplings (intrinsic and Rashba). The wedge disclination changes the flat lattice into the conical lattice and hence modifies the spin orbit couplings. The Hamiltonian is exactly solved for the intrinsic spin orbit interaction and perturbatively for the Rashba spin orbit interaction. It is shown that there exists the Kramer's degenerate midgap localized spin separated fluxon states around the defect. These zero energy spin separated states occur at the external magnetic flux value $\Phi\pm\Delta\Phi$. The external magnetic flux $\Phi$ is introduced to make the wave-function periodic when the electron circulates around the defect. It is found that this separation occurs due to the effect of the conical curvature on the spin orbit coupling. Further, we find these results are robust to the addition of the Rashba spin orbit interaction which is important for the application to spintronics and nanoelectronics.Comment: 6 pages ,3 figures ,Change in titl

Correlation, Network and Multifractal Analysis of Global Financial Indices

We apply RMT, Network and MF-DFA methods to investigate correlation, network and multifractal properties of 20 global financial indices. We compare results before and during the financial crisis of 2008 respectively. We find that the network method gives more useful information about the formation of clusters as compared to results obtained from eigenvectors corresponding to second largest eigenvalue and these sectors are formed on the basis of geographical location of indices. At threshold 0.6, indices corresponding to Americas, Europe and Asia/Pacific disconnect and form different clusters before the crisis but during the crisis, indices corresponding to Americas and Europe are combined together to form a cluster while the Asia/Pacific indices forms another cluster. By further increasing the value of threshold to 0.9, European countries France, Germany and UK constitute the most tightly linked markets. We study multifractal properties of global financial indices and find that financial indices corresponding to Americas and Europe almost lie in the same range of degree of multifractality as compared to other indices. India, South Korea, Hong Kong are found to be near the degree of multifractality of indices corresponding to Americas and Europe. A large variation in the degree of multifractality in Egypt, Indonesia, Malaysia, Taiwan and Singapore may be a reason that when we increase the threshold in financial network these countries first start getting disconnected at low threshold from the correlation network of financial indices. We fit Binomial Multifractal Model (BMFM) to these financial markets.Comment: 32 pages, 25 figures, 1 tabl

Symmetry Breaking in the Double-Well Hermitian Matrix Models

We study symmetry breaking in $Z_2$ symmetric large $N$ matrix models. In the planar approximation for both the symmetric double-well $\phi^4$ model and the symmetric Penner model, we find there is an infinite family of broken symmetry solutions characterized by different sets of recursion coefficients $R_n$ and $S_n$ that all lead to identical free energies and eigenvalue densities. These solutions can be parameterized by an arbitrary angle $\theta(x)$, for each value of $x = n/N < 1$. In the double scaling limit, this class reduces to a smaller family of solutions with distinct free energies already at the torus level. For the double-well $\phi^4$ theory the double scaling string equations are parameterized by a conserved angular momentum parameter in the range $0 \le l < \infty$ and a single arbitrary $U(1)$ phase angle.Comment: 23 pages and 4 figures, Preprint No. CERN-TH.6611/92, Brown HET-863, HUTP -- 92/A035, LPTHE-Orsay: 92/2

Spectral Statistics of Instantaneous Normal Modes in Liquids and Random Matrices

We study the statistical properties of eigenvalues of the Hessian matrix ${\cal H}$ (matrix of second derivatives of the potential energy) for a classical atomic liquid, and compare these properties with predictions for random matrix models (RMM). The eigenvalue spectra (the Instantaneous Normal Mode or INM spectra) are evaluated numerically for configurations generated by molecular dynamics simulations. We find that distribution of spacings between nearest neighbor eigenvalues, s, obeys quite well the Wigner prediction $s exp(-s^2)$, with the agreement being better for higher densities at fixed temperature. The deviations display a correlation with the number of localized eigenstates (normal modes) in the liquid; there are fewer localized states at higher densities which we quantify by calculating the participation ratios of the normal modes. We confirm this observation by calculating the spacing distribution for parts of the INM spectra with high participation ratios, obtaining greater conformity with the Wigner form. We also calculate the spectral rigidity and find a substantial dependence on the density of the liquid.Comment: To appear in Phys. Rev. E; 10 pages, 6 figure

Comparison of glucosamine sulfate and a polyherbal supplement for the relief of osteoarthritis of the knee: a randomized controlled trial [ISRCTN25438351]

<p>Abstract</p> <p>Background</p> <p>The efficacy and safety of a dietary supplement derived from South American botanicals was compared to glucosamine sulfate in osteoarthritis subjects in a Mumbai-based multi-center, randomized, double-blind study.</p> <p>Methods</p> <p>Subjects (n = 95) were screened and randomized to receive glucosamine sulfate (n = 47, 1500 mg/day) or reparagen (n = 48, 1800 mg/day), a polyherbal consisting of 300 mg of vincaria (<it>Uncaria guianensis</it>) and 1500 mg of RNI 249 (<it>Lepidium meyenii</it>) administered orally, twice daily. Primary efficacy variable was response rate based on a 20% improvement in WOMAC pain scores. Additional outcomes were WOMAC scores for pain, stiffness and function, visual analog score (VAS) for pain, with assessments at 1, 2, 4, 6 and 8 weeks. Tolerability, investigator and subject global assessments and rescue medication consumption (paracetamol) were measured together with safety assessments including vital signs and laboratory based assays.</p> <p>Results</p> <p>Subject randomization was effective: age, gender and disease status distribution was similar in both groups. The response rates (20% reduction in WOMAC pain) were substantial for both glucosamine (89%) and reparagen (94%) and supported by investigator and subject assessments. Using related criteria response rates to reparagen were favorable when compared to glucosamine. Compared to baseline both treatments showed significant benefits in WOMAC and VAS outcomes within one week (P < 0.05), with a similar, progressive improvement over the course of the 8 week treatment protocol (45–62% reduction in WOMAC or VAS scores). Tolerability was excellent, no serious adverse events were noted and safety parameters were unchanged. Rescue medication use was significantly lower in the reparagen group (p < 0.01) at each assessment period. Serum IGF-1 levels were unaltered by treatments.</p> <p>Conclusion</p> <p>Both reparagen and glucosamine sulfate produced substantial improvements in pain, stiffness and function in subjects with osteoarthritis. Response rates were high and the safety profile was excellent, with significantly less rescue medication use with reparagen. Reparagen represents a new natural productive alternative in the management of joint health.</p> <p>Trial registration</p> <p>Current Controlled Trials ISRCTN25438351.</p

Anomalies

This thesis studies the structure of local and global anomalies in certain systems and examines the conditions for their cancellation. Gauge anomalies-abelian and non-albelian-antisymmetric tensor, and gravitational anomalies in simple spinor theories with background fields have been analyzed by perturbative methods and local counterterms have been constructed to cancel the anomalies wherever possible. Anomalies occurring in supersymmetric theories in (2 + 1)-dimensions have also been calculated using both perturbative and heat kernel techniques, here again counterterms have been constructed to cancel these parity violating anomalies for certain gauge field configurations. (i) For gauge theories in four dimensions which contain couplings of fermions to a non-abelian antisymmetric tensor field, the contribution of the later to anomalies in the non-abelian chiral Ward identity is computed. It is shown by explicit construction of suitable counterterms that these anomalies can all be cancelled. (ii) The gauge anomalies associated with the gravitational fields in abelian gauge theories can be completely removed provided torsion is nonzero. This is shown by constructing a counterterm associated with the gravitational Goldstone-Wilczek current which cancels the anomalous gravitational contribution to the chiral Ward identity without introducing anomalies in the Lorentz or Einstein Ward identities. (iii) Using perturbative BPHZ renormalization techniques the parity odd part of the effective action has been extracted and explicitly determined for abitrary non-abelian gauge superfields in odd dimensions and shown to be the supersymmetric Chern-Simons secondary topological invariant. (iv) Schwinger\u27s proper time technique is generalized to supersymmetric theories in odd dimensions. The effective action for supersymmetric QED is exactly found for space-time constant superfield. The parity violating anomaly induced in the effective action can be cancelled by adding a local counterterm. (v) A pair of gauge superfield configurations in supersymmetric non-abelian gauge theories in (2 + 1)-dimensions which exhibit the Wu-Yang ambiguity are identified and the effective action computed exactly for one of them, in analogy with (iv). Both configurations give rise to a parity anomaly in the effective action which cannot be removed by the addition of a counterterm

Crossover eigenvalue correlators using Dyson-Schwinger loop equations

The coupled two-matrix model is studied in the case of one of the matrices belonging to the orthogonal ensemble and the other one belonging to the unitary ensemble, using the Dyson- Schwinger equations or loop equations. The loop equations form an infinite hierarchy which becomes a closed set of algebraic equations in the large-N limit. This allows for the determination of correlation functions of loop operators and the eigenvalue correlators of the model. In particular, we determine the density-density correlators relevant in models of quantum chaos where crossover from one symmetry class to another occurs. The method gives smoothed global correlators