Multi-Instantons and Multi-Cuts

We discuss various aspects of multi-instanton configurations in generic multi-cut matrix models. Explicit formulae are presented in the two-cut case and, in particular, we obtain general formulae for multi-instanton amplitudes in the one-cut matrix model case as a degeneration of the two-cut case. These formulae show that the instanton gas is ultra-dilute, due to the repulsion among the matrix model eigenvalues. We exemplify and test our general results in the cubic matrix model, where multi-instanton amplitudes can be also computed with orthogonal polynomials. As an application, we derive general expressions for multi-instanton contributions in two-dimensional quantum gravity, verifying them by computing the instanton corrections to the string equation. The resulting amplitudes can be interpreted as regularized partition functions for multiple ZZ-branes, which take into full account their back-reaction on the target geometry. Finally, we also derive structural properties of the trans-series solution to the Painleve I equation.Comment: 34 pages, 3 figures, JHEP3.cls; v2: added references, minor changes; v3: added 1 reference, more minor changes, final version for JMP; v4: more typos correcte

The friendship paradox in scale-free networks

Our friends have more friends than we do. That is the basis of the friendship paradox. In mathematical terms, the mean number of friends of friends is higher than the mean number of friends. In the present study, we analyzed the relationship between the mean degree of vertices (individuals), , and the mean number of friends of friends, , in scale-free networks with degrees ranging from a minimum degree (k_min) to a maximum degree (k_max). We deduced an expression for - for scale-free networks following a power-law distribution with a given scaling parameter (alpha). Based on this expression, we can quantify how the degree distribution of a scale-free network affects the mean number of friends of friends.Comment: 9 pages, 2 figure

Multipartite Entanglement Signature of Quantum Phase Transitions

We derive a general relation between the non-analyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by T. R. de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.Comment: Published version. Incorporates correction made in erratu

Detecting photon-photon scattering in vacuum at exawatt lasers

In a recent paper, we have shown that the QED nonlinear corrections imply a phase correction to the linear evolution of crossing electromagnetic waves in vacuum. Here, we provide a more complete analysis, including a full numerical solution of the QED nonlinear wave equations for short-distance propagation in a symmetric configuration. The excellent agreement of such a solution with the result that we obtain using our perturbatively-motivated Variational Approach is then used to justify an analytical approximation that can be applied in a more general case. This allows us to find the most promising configuration for the search of photon-photon scattering in optics experiments. In particular, we show that our previous requirement of phase coherence between the two crossing beams can be released. We then propose a very simple experiment that can be performed at future exawatt laser facilities, such as ELI, by bombarding a low power laser beam with the exawatt bump.Comment: 8 pages, 6 figure

Transport properties of chemically synthesized polypyrrole thin films

The electronic transport in polypyrrole thin films synthesized chemically from the vapor phase is studied as a function of temperature as well as of electric and magnetic fields. We find distinct differences in comparison to the behavior of both polypyrrole films prepared by electrochemical growth as well as of the bulk films obtained from conventional chemical synthesis. For small electric fields F, a transition from Efros-Shklovskii variable range hopping to Arrhenius activated transport is observed at 30 K. High electric fields induce short range hopping. The characteristic hopping distance is found to be proportional to F^(-1/2). The magnetoresistance R(B) is independent of F below a critical magnetic field, above which F counteracts the magnetic field induced localization.Comment: 6 pages, 5 figure

Operational Classification and Quantification of Multipartite Entangled States

We formalize and extend an operational multipartite entanglement measure introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006), through the generalization of global entanglement (GE) [D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field, being thus able to detect a quantum phase transition.Comment: 14 pages, RevTex4, published versio

Direct minimally invasive enzymatic determination of tyramine in cheese using digital imaging

An enzymatic method for the direct (without pretreatment) minimally invasive tyramine determination in cheese is proposed. Colorimetric test strips containing tyramine oxidase (TAO), peroxidase and 3, 3', 5, 5'-tetramethylbenzidine (Q-TAO), allow tyramine determination through the RGB chromatic coordinates of the observed blue colour (LOD = 2.6·10-6 M, LOQ = 8.7·10-6 M, RSD% (n = 5; 1.8·10-4 M) = 3.2%). The strips are inserted in the sample for 2 min and then the RGB coordinates are measured using a smartphone. Previously, these Q-TAO strips have been also optimized for tyramine determination in cheese extract. To do that, a spectrophotometric method in solution for tyramine determination in cheese extracts has been developed, which included an in-depth study of the indicating reaction; this study has allowed to gain new information about the spectroscopic properties of different TMB species and, which it is more important, to detect cross-reactions between TAO and TMB species. A mathematical model has also been developed which relate the RGB signals obtained with the tyramine concentrations, the instrumental characteristics of the smartphone and the spectroscopic properties of the absorbing product of the enzymatic reaction. © 2021 Elsevier B.V

The intrinsic fluorescence of FAD and its application in analytical chemistry: a review

This review (with 106 references) mainly deals with the analytical applications of flavin-adenine dinucleotide (FAD) fluorescence. In the first section, the spectroscopic properties of this compound are reviewed at the light of his different acid-base, oxidation and structural forms; the chemical and spectroscopic properties of flavin mononucleotide (FMN) and other flavins will be also briefly discussed. The second section discusses how the properties of FAD fluorescence changes in flavoenzymes (FvEs), again considering the different chemical and structural forms; the glucose oxidase (GOx) and the choline oxidase (ChOx) cases will be commented. Since almost certainly the most reported analytical application of FAD fluorescence is as an auto-indicator in enzymatic methods catalysed by FvE oxidoreductases, it is important to know how the concentrations of the different forms of FAD changes along the reaction and, consequently, the fluorescence and the analytical signals. An approach to do this will be presented in section 3. The fourth part of the paper compiles the analytical applications which have been reported until now based in these fluorescence properties. Finally, some suggestions about tentative future research are also given