Large NN expansion of Wilson loops in the Gross-Witten-Wadia matrix model

We study the large $N$ expansion of winding Wilson loops in the off-critical regime of the Gross-Witten-Wadia (GWW) unitary matrix model. These have been recently considered in arXiv:1705.06542 and computed by numerical methods. We present various analytical algorithms for the precise computation of both the perturbative and instanton corrections to the Wilson loops. In the gapped phase of the GWW model we present the genus five expansion of the one-cut resolvent that captures all winding loops. Then, as a complementary tool, we apply the Periwal-Shevitz orthogonal polynomial recursion to the GWW model coupled to suitable sources and show how it generates all higher genus corrections to any specific loop with given winding. The method is extended to the treatment of instanton effects including higher order $1/N$ corrections. Several explicit examples are fully worked out and a general formula for the next-to-leading correction at general winding is provided. For the simplest cases, our calculation checks exact results from the Schwinger-Dyson equations, but the presented tools have a wider range of applicability.Comment: 28 pages, 3 pdf figures. v2: minor additions, extended reference

Charge transport in bacteriorhodopsin monolayers: The contribution of conformational change to current-voltage characteristics

When moving from native to light activated bacteriorhodopsin, modification of charge transport consisting of an increase of conductance is correlated to the protein conformational change. A theoretical model based on a map of the protein tertiary structure into a resistor network is implemented to account for a sequential tunneling mechanism of charge transfer through neighbouring amino acids. The model is validated by comparison with current-voltage experiments. The predictability of the model is further tested on bovine rhodopsin, a G-protein coupled receptor (GPCR) also sensitive to light. In this case, results show an opposite behaviour with a decrease of conductance in the presence of light.Comment: 6 pages, 4 figure

Distribution of Return Periods of Rare Events in Correlated Time Series

We study the effect on the distribution of return periods of rare events of the presence in a time series of finite-term correlations with non-exponential decay. Precisely, we analyze the auto-correlation function and the statistics of the return intervals of extreme values of the resistance fluctuations displayed by a resistor with granular structure in a nonequilibrium stationary state. The resistance fluctuations, $\delta R$, are calculated by Monte Carlo simulations using the SBRN model introduced some years ago by Pennetta, Tref\'an and Reggiani and based on a resistor network approach. A rare event occurs when $\delta R$ overcomes a threshold value $q$ significantly higher than the average value of the resistance. We have found that for highly disordered networks, when the auto-correlation function displays a non-exponential decay but yet the resistance fluctuations are characterized by a finite correlation time, the distribution of return intervals of the extreme values is well described by a stretched exponential, with exponent largely independent of the threshold $q$. We discuss this result and some of the main open questions related to it, also in connection with very recent findings by other authors concerning the observation of stretched exponential distributions of return intervals of extreme events in long-term correlated time series.Comment: 10 pages, 8 figures, Procs. of 4th. Int. Conf. on Unsolved Problems on Noise and Fluctuations in Physics, Biology and High Technology (UPoN05), 6-10 June 2005, Gallipoli (Italy), AIP Conf. Procs. (in print

Time-reversal violation as loop-antiloop symmetry breaking: the Bessel equation, group contraction and dissipation

We show that the Bessel equation can be cast, by means of suitable transformations, into a system of two damped/amplified parametric oscillator equations. The relation with the group contraction mechanism is analyzed and the breakdown of loop-antiloop symmetry due to group contraction manifests itself as violation of time-reversal symmetry. A preliminary discussion of the relation between some infinite dimensional loop-algebras, such as the Virasoro-like algebra, and the Euclidean algebras e(2) and e(3) is also presented.Comment: 15 pages, Late

Duality and reciprocity of fluctuation-dissipation relations in conductors

By analogy with linear-response we formulate the duality and reciprocity properties of current and voltage fluctuations expressed by Nyquist relations including the intrinsic bandwidths of the respective fluctuations. For this purpose we individuate total-number and drift-velocity fluctuations of carriers inside a conductor as the microscopic sources of noise. The spectral densities at low frequency of the current and voltage fluctuations and the respective conductance and resistance are related in a mutual exclusive way to the corresponding noise-source. The macroscopic variance of current and voltage fluctuations are found to display a dual property via a plasma conductance that admits a reciprocal plasma resistance. Analogously, the microscopic noise-sources are found to obey a dual property and a reciprocity relation. The formulation is carried out in the frame of the grand canonical (for current noise) and canonical (for voltage noise) ensembles and results are derived which are valid for classical as well as for degenerate statistics including fractional exclusion statistics. The unifying theory so developed sheds new light on the microscopic interpretation of dissipation and fluctuation phenomena in conductors. In particular it is proven that, as a consequence of the Pauli principle, for Fermions non-vanishing single-carrier velocity fluctuations at zero temperature are responsible for diffusion but not for current noise, which vanishes in this limit.Comment: 5 pages, 1 figur

Charge transport in purple membrane monolayers: A sequential tunneling approach

Current voltage (I-V) characteristics in proteins can be sensitive to conformational change induced by an external stimulus (photon, odour, etc.). This sensitivity can be used in medical and industrial applications besides shedding new light in the microscopic structure of biological materials. Here, we show that a sequential tunneling model of carrier transfer between neighbouring amino-acids in a single protein can be the basic mechanism responsible of the electrical properties measured in a wide range of applied potentials. We also show that such a strict correlation between the protein structure and the electrical response can lead to a new generation of nanobiosensors that mimic the sensorial activity of living species. To demonstrate the potential usefulness of protein electrical properties, we provide a microscopic interpretation of recent I-V experiments carried out in bacteriorhodopsin at a nanoscale length.Comment: 4 pages, 4 figure

Reactive immunization on complex networks

Epidemic spreading on complex networks depends on the topological structure as well as on the dynamical properties of the infection itself. Generally speaking, highly connected individuals play the role of hubs and are crucial to channel information across the network. On the other hand, static topological quantities measuring the connectivity structure are independent on the dynamical mechanisms of the infection. A natural question is therefore how to improve the topological analysis by some kind of dynamical information that may be extracted from the ongoing infection itself. In this spirit, we propose a novel vaccination scheme that exploits information from the details of the infection pattern at the moment when the vaccination strategy is applied. Numerical simulations of the infection process show that the proposed immunization strategy is effective and robust on a wide class of complex networks

Generalized Gumbel distribution of current fluctuations in purple membrane monolayers

We investigate the nature of a class of probability density functions, say G(a), with a the shape parameter, which generalizes the Gumbel distribution. These functions appear in a model of charge transport, when applied to a metal-insulator-metal structure, where the insulator is constituted by a monolayer of bacteriorhodopsin. Current shows a sharp increase above about 3 V, interpreted as the cross-over between direct and injection sequential-tunneling regimes. In particular, we show that, changing the bias value, the probability density function changes its look from bimodal to unimodal. Actually, the bimodal distributions can be resolved in at least a couple of $G(a)$ functions with different values of the shape parameter.Comment: 5 pages, 6 figure

Beyond the Formulations of the Fluctuation Dissipation Theorem Given by Callen and Welton (1951) and Expanded by Kubo (1966)

The quantum formula of the fluctuation dissipation theorem (FDT) was given by Callen and Welton in 1951 [1] for the case of conductors, and then expanded by Kubo in 1966 [2, 3]. The drawback of these quantum relations concerns with the appearance of a zero-point contribution, hω/2 with h the reduced Planck constant and ω the angular frequency of the considered photon, which implies a divergence of the fluctuation spectrum at increasing frequencies. This divergence is responsible for a vacuum-catastrophe, to keep the analogy with the well-known ultraviolet catastrophe of the classical black-body radiation spectrum. As a consequence, the quantum formulation of the FDT as given by CallenWelton and Kubo introduces a Field Grand Challenge associated with the existence or less of a vacuum-fluctuations catastrophe for the energy-density spectrum. Here we propose a solution to this challenge by taking into account of the Casimir energy that, in turns, is found to be responsible for a quantum correction of the Stefan-Boltzmann la