Universal eigenvector statistics in a quantum scattering ensemble

We calculate eigenvector statistics in an ensemble of non-Hermitian matrices describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in the limit of large matrix size. We show that ensemble-averaged eigenvector correlations corresponding to eigenvalues in the center of the support of the density of states in the complex plane are described by an expression recently derived for Ginibre's ensemble of random non-Hermitian matrices.Comment: 4 pages, 5 figure

Photo-responsive polymer with erasable and reconfigurable micro- and nano-patterns: An in vitro study for neuron guidance

The interaction of cells with nanoscale topography has proven to be an important modality in controlling cell responses. Topographic parameters on material surfaces play a role in cell growth. We have synthesized a new bio compatible polymer containing photoswitching molecules. Stripepatterned (groove/ridge pattern) were patterned and erased with ease on this bio azopolymer with two different set-ups: one with the projection of an optical interference pattern and the other one by molecular self-organization with one single laser beam. These two set-ups allow the re-writing of pattern after erasing and its inscription in vitro. PC12 cells were cultured on the bio-photoswitching patterned polymer and compared with PC12 cells growing on a well know substrate: poly-L-lysine. This result is of interest for facilitating contact guidance and designing reconfigurable scaffold for neural network formation in vitro. (C) 2011 Elsevier B.V. All rights reserve

Eigenvector statistics in non-Hermitian random matrix ensembles

We study statistical properties of the eigenvectors of non-Hermitian random matrices, concentrating on Ginibre's complex Gaussian ensemble, in which the real and imaginary parts of each element of an N x N matrix, J, are independent random variables. Calculating ensemble averages based on the quantity $< L_\alpha | L_\beta >$, where $< L_\alpha |$ and $| R_\beta >$ are left and right eigenvectors of J, we show for large N that eigenvectors associated with a pair of eigenvalues are highly correlated if the two eigenvalues lie close in the complex plane. We examine consequences of these correlations that are likely to be important in physical applications.Comment: 4 pages, no figure

Fermion determinants in matrix models of QCD at nonzero chemical potential

The presence of a chemical potential completely changes the analytical structure of the QCD partition function. In particular, the eigenvalues of the Dirac operator are distributed over a finite area in the complex plane, whereas the zeros of the partition function in the complex mass plane remain on a curve. In this paper we study the effects of the fermion determinant at nonzero chemical potential on the Dirac spectrum by means of the resolvent, G(z), of the QCD Dirac operator. The resolvent is studied both in a one-dimensional U(1) model (Gibbs model) and in a random matrix model with the global symmetries of the QCD partition function. In both cases we find that, if the argument z of the resolvent is not equal to the mass m in the fermion determinant, the resolvent diverges in the thermodynamic limit. However, for z =m the resolvent in both models is well defined. In particular, the nature of the limit $z \rightarrow m$ is illuminated in the Gibbs model. The phase structure of the random matrix model in the complex m and \mu-planes is investigated both by a saddle point approximation and via the distribution of Yang-Lee zeros. Both methods are in complete agreement and lead to a well-defined chiral condensate and quark number density.Comment: 27 pages, 6 figures, Late

Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics

By using the method of orthogonal polynomials we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from Hermitian matrices characterized by the Wigner- Dyson statistics of real eigenvalues to strongly non-Hermitian ones whose complex eigenvalues were studied by Ginibre. Two-point statistical measures (as e.g. spectral form factor, number variance and small distance behavior of the nearest neighbor distance distribution $p(s)$) are studied in more detail. In particular, we found that the latter function may exhibit unusual behavior $p(s)\propto s^{5/2}$ for some parameter values.Comment: 4 pages, RevTE

Exact Superpotentials, Theories with Flavor and Confining Vacua

In this paper we study some interesting properties of the effective superpotential of N=1 supersymmetric gauge theories with fundamental matter, with the help of the Dijkgraaf--Vafa proposal connecting supersymmetric gauge theories with matrix models. We find that the effective superpotential for theories with N_f fundamental flavors can be calculated in terms of quantities computed in the pure (N_f=0) gauge theory. Using this property we compute in a remarkably simple way the exact effective superpotential of N=1 supersymmetric theories with fundamental matter and gauge group SU(N_c), at the point in the moduli space where a maximal number of monopoles become massless (confining vacua). We extend the analysis to a generic point of the moduli space, and show how to compute the effective superpotential in this general case.Comment: 16 pages, no figure

Infinite N phase transitions in continuum Wilson loop operators

We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth loop is dilated from a small size to a large one. If this large N phase transition belongs to a solvable universality class one might be able to calculate analytically the string tension in terms of the perturbative Lambda-parameter. This would be achieved by matching instanton results for small loops to the relevant large-N-universal function which, in turn, would be matched for large loops to an effective string theory. Similarities between our findings and known analytical results in two dimensional space-time indicate that the phase transitions we found only affect the eigenvalue distribution, but the traces of finite powers of the Wilson loop operators stay smooth under scaling.Comment: 31 pages, 9 figures, typos and references corrected, minor clarifications adde

Investigating the microbial community of Cacopsylla spp. as potential factor in vector competence of phytoplasma

Phytoplasmas are obligatory intracellular bacteria that colonize the phloem of many plant species and cause hundreds of plant diseases worldwide. In nature, phytoplasmas are primarily transmitted by hemipteran vectors. While all phloem-feeding insects could in principle transmit phytoplasmas, only a limited number of species have been confirmed as vectors. Knowledge about factors that might determine the vector capacity is currently scarce. Here, we characterized the microbiomes of vector and non-vector species of apple proliferation (AP) phytoplasma ‘Candidatus Phytoplasma mali’ to investigate their potential role in the vector capacity of the host. We performed high-throughput 16S rRNA metabarcoding of the two principal AP-vectors Cacopsylla picta and Cacopsylla melanoneura and eight Cacopsylla species, which are not AP-vectors but co-occur in apple orchards. The microbiomes of all species are dominated by Carsonella, the primary endosymbiont of psyllids and a second uncharacterized Enterobacteriaceae endosymbiont. Each Cacopsylla species harboured a speciesspecific phylotype of both symbionts. Moreover, we investigated differences between the microbiomes of AP-vector versus non-vector species and identified the predominant endosymbionts but also Wolbachia and several minor taxa as potential indicator species. Our study highlights the importance of considering the microbiome in future investigations of potential factors influencing host vector competence. We investigated the potential role of symbiotic bacteria in the acquisition and transmission of phytoplasma. By comparing the two main psyillid vector species of Apple proliferation (AP) phytoplasma and eight co-occurring species, which are not able to vector AP-phytoplasma, we found differences in the microbial communities of AP-vector and non-vector species, which appear to be driven by the predominant symbionts in both vector species and Wolbachia and several minor taxa in the non-vector species. In contrast, infection with APphytoplasma did not affect microbiome composition in both vector species. Our study provides new insights into the endosymbiont diversity of Cacopsylla spp. and highlights the importance of considering the microbiome when investigating potential factors influencing host vector competenc

A Random Matrix Approach to VARMA Processes

We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N/T is fixed. In this regime the underlying random matrices are asymptotically equivalent to Free Random Variables (FRV). We apply the FRV calculus to calculate the eigenvalue density of the sample covariance for several VARMA-type processes. We explicitly solve the VARMA(1,1) case and demonstrate a perfect agreement between the analytical result and the spectra obtained by Monte Carlo simulations. The proposed method is purely algebraic and can be easily generalized to q1>1 and q2>1.Comment: 16 pages, 6 figures, submitted to New Journal of Physic

Matrix Models, Monopoles and Modified Moduli

Motivated by the Dijkgraaf-Vafa correspondence, we consider the matrix model duals of N=1 supersymmetric SU(Nc) gauge theories with Nf flavors. We demonstrate via the matrix model solutions a relation between vacua of theories with different numbers of colors and flavors. This relation is due to an N=2 nonrenormalization theorem which is inherited by these N=1 theories. Specializing to the case Nf=Nc, the simplest theory containing baryons, we demonstrate that the explicit matrix model predictions for the locations on the Coulomb branch at which monopoles condense are consistent with the quantum modified constraints on the moduli in the theory. The matrix model solutions include the case that baryons obtain vacuum expectation values. In specific cases we check explicitly that these results are also consistent with the factorization of corresponding Seiberg-Witten curves. Certain results are easily understood in terms of M5-brane constructions of these gauge theories.Comment: 27 pages, LaTeX, 2 figure