Non-Gaussianity of resistance fluctuations near electrical breakdown

We study the resistance fluctuation distribution of a thin film near electrical breakdown. The film is modeled as a stationary resistor networkunder biased percolation. Depending on the value of the external current,on the system sizes and on the level of internal disorder, the fluctuation distribution can exhibit a non-Gaussian behavior. We analyze this non-Gaussianity in terms of the generalized Gumbel distribution recently introduced in the context of highly correlated systems near criticality. We find that when the average fraction of defects approaches the random percolation threshold, the resistance fluctuation distribution is well described by the universal behavior of the Bramwell-Holdsworth-Pinton distribution.Comment: 3 figures, accepted for publication on Semicond Sci Tec

Non-Gaussian Fluctuations in Biased Resistor Networks: Size Effects versus Universal Behavior

We study the distribution of the resistance fluctuations of biased resistor networks in nonequilibrium steady states. The stationary conditions arise from the competition between two stochastic and biased processes of breaking and recovery of the elementary resistors. The fluctuations of the network resistance are calculated by Monte Carlo simulations which are performed for different values of the applied current, for networks of different size and shape and by considering different levels of intrinsic disorder. The distribution of the resistance fluctuations generally exhibits relevant deviations from Gaussianity, in particular when the current approaches the threshold of electrical breakdown. For two-dimensional systems we have shown that this non-Gaussianity is in general related to finite size effects, thus it vanishes in the thermodynamic limit, with the remarkable exception of highly disordered networks. For these systems, close to the critical point of the conductor-insulator transition, non-Gaussianity persists in the large size limit and it is well described by the universal Bramwell-Holdsworth-Pinton distribution. In particular, here we analyze the role of the shape of the network on the distribution of the resistance fluctuations. Precisely, we consider quasi-one-dimensional networks elongated along the direction of the applied current or trasversal to it. A significant anisotropy is found for the properties of the distribution. These results apply to conducting thin films or wires with granular structure stressed by high current densities.Comment: 8 pages, 4 figures. Invited talk at the 18-th International Conference on Noise and Fluctuations, 19-23 September 2005, Salamanc

A network model to investigate structural and electrical properties of proteins

One of the main trend in to date research and development is the miniaturization of electronic devices. In this perspective, integrated nanodevices based on proteins or biomolecules are attracting a major interest. In fact, it has been shown that proteins like bacteriorhodopsin and azurin, manifest electrical properties which are promising for the development of active components in the field of molecular electronics. Here we focus on two relevant kinds of proteins: The bovine rhodopsin, prototype of GPCR protein, and the enzyme acetylcholinesterase (AChE), whose inhibition is one of the most qualified treatments of Alzheimer disease. Both these proteins exert their functioning starting with a conformational change of their native structure. Our guess is that such a change should be accompanied with a detectable variation of their electrical properties. To investigate this conjecture, we present an impedance network model of proteins, able to estimate the different electrical response associated with the different configurations. The model resolution of the electrical response is found able to monitor the structure and the conformational change of the given protein. In this respect, rhodopsin exhibits a better differential response than AChE. This result gives room to different interpretations of the degree of conformational change and in particular supports a recent hypothesis on the existence of a mixed state already in the native configuration of the protein.Comment: 25 pages, 12 figure

A class of nonlinear wave equations containing the continuous Toda case

We consider a nonlinear field equation which can be derived from a binomial lattice as a continuous limit. This equation, containing a perturbative friction-like term and a free parameter $\gamma$, reproduces the Toda case (in absence of the friction-like term) and other equations of physical interest, by choosing particular values of $\gamma$. We apply the symmetry and the approximate symmetry approach, and the prolongation technique. Our main purpose is to check the limits of validity of different analytical methods in the study of nonlinear field equations. We show that the equation under investigation with the friction-like term is characterized by a finite-dimensional Lie algebra admitting a realization in terms of boson annhilation and creation operators. In absence of the friction-like term, the equation is linearized and connected with equations of the Bessel type. Examples of exact solutions are displayed, and the algebraic structure of the equation is discussed.Comment: Latex file + [equations.sty], 22 p

Vacuum structure for expanding geometry

We consider gravitational wave modes in the FRW metrics in a de Sitter phase and show that the state space splits into many unitarily inequivalent representations of the canonical commutation relations. Non-unitary time evolution is described as a trajectory in the space of the representations. The generator of time evolution is related to the entropy operator. The thermodynamic arrow of time is shown to point in the same direction of the cosmological arrow of time. The vacuum is a two-mode SU(1,1) squeezed state of thermo field dynamics. The link between expanding geometry, squeezing and thermal properties is exhibited.Comment: Latex file, epsfig, 1 figure, 21 page

Tuning the Correlation Decay in the Resistance Fluctuations of Multi-Species Networks

A new network model is proposed to describe the $1/f^\alpha$ resistance noise in disordered materials for a wide range of $\alpha$ values ($0< \alpha < 2$). More precisely, we have considered the resistance fluctuations of a thin resistor with granular structure in different stationary states: from nearly equilibrium up to far from equilibrium conditions. This system has been modelled as a network made by different species of resistors, distinguished by their resistances, temperature coefficients and by the energies associated with thermally activated processes of breaking and recovery. The correlation behavior of the resistance fluctuations is analyzed as a function of the temperature and applied current, in both the frequency and time domains. For the noise frequency exponent, the model provides $0< \alpha < 1$ at low currents, in the Ohmic regime, with $\alpha$ decreasing inversely with the temperature, and $1< \alpha <2$ at high currents, in the non-Ohmic regime. Since the threshold current associated with the onset of nonlinearity also depends on the temperature, the proposed model qualitatively accounts for the complicate behavior of $\alpha$ versus temperature and current observed in many experiments. Correspondingly, in the time domain, the auto-correlation function of the resistance fluctuations displays a variety of behaviors which are tuned by the external conditions.Comment: 26 pages, 16 figures, Submitted to JSTAT - Special issue SigmaPhi200

Non-Gaussian Resistance Noise near Electrical Breakdown in Granular Materials

The distribution of resistance fluctuations of conducting thin films with granular structure near electrical breakdown is studied by numerical simulations. The film is modeled as a resistor network in a steady state determined by the competition between two biased processes, breaking and recovery. Systems of different sizes and with different levels of internal disorder are considered. Sharp deviations from a Gaussian distribution are found near breakdown and the effect increases with the degree of internal disorder. However, we show that in general this non-Gaussianity is related to the finite size of the system and vanishes in the large size limit. Nevertheless, near the critical point of the conductor-insulator transition, deviations from Gaussianity persist when the size is increased and the distribution of resistance fluctuations is well fitted by the universal Bramwell-Holdsworth-Pinton distribution.Comment: 8 pages, 6 figures; accepted for publication on Physica

Non-Gaussian Resistance Fluctuations in Disordered Materials

ABSTRACT We study the distribution of resistance fluctuations of conducting thin films with different levels of internal disorder. The film is modeled as a resistor network in a steady state determined by the competition between two biased processes, breaking and recovery of the elementary resistors. The fluctuations of the film resistance are calculated by Monte Carlo simulations which are performed under different bias conditions, from the linear regime up to the threshold for electrical breakdown. Depending on the value of the external current, on the level of disorder and on the size of the system, the distribution of the resistance fluctuations can exhibit significant deviations from Gaussianity. As a general trend, a size dependent, non universal distribution is found for systems with low and intermediate disorder. However, for strongly disordered systems, close to the critical point of the conductor-insulator transition, the non-Gaussianity persists when the size is increased and the distribution of resistance fluctuations is well described by the universal Bramwell-Holdsworth-Pinton distribution

Remarks on flavor-neutrino propagators and oscillation formulae

We examine the general structure of the formulae of neutrino oscillations proposed by Blasone and Vitiello(BV). Reconstructing their formulae with the retarded propagators of the flavor neutrino fields for the case of many flavors, we can get easily the formulae which satisfy the suitable boundary conditions and are independent of arbitrary mass parameters $\{\mu_{\rho}\}$, as is obtained by BV for the case of two flavors. In this two flavor case, our formulae reduce to those obtained by BV under $T$-invariance condition. Furthermore, the reconstructed probabilities are shown to coincide with those derived with recourse to the mass Hilbert space ${\cal H}_{m}$ which is unitarily inequivalent to the flavor Hilbert space ${\cal H}_{f}$. Such a situation is not found in the corresponding construction a la BV. Then the new factors in the BV's formulae, which modify the usual oscill ation formulae, are not the trace of the flavor Hilbert space construction, but come from Bogolyubov transformation among the operators of spin-1/2 ne utrino with different masses.Comment: revtex, 16 page

A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order "conservation laws". In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system), and the lattice Heisenberg ferromagnet model. For the Volterra lattice and modified Volterra lattice, we also present their ultradiscrete analogues.Comment: 61 pages; (v2)(v3) many minor correction