[en] Full text: Mesoscopic physics is emerging as the basis for a new technology. Although very successful theories of electrical transport at near-nanometre scales are available, describing current-noise behaviour in the same regime is not straightforward. Given that practical mesoscopic electronics must deal with a much larger role played by charge fluctuations, the time is well ripe for a more rigorous attack on these problems. Here we survey a few of the issues confronting mesoscopic noise physics, the existing phenomenological approaches, and a promising microscopic model based on a kinetic approach. Finally we discuss some outstanding theoretical and experimental questions. Examples are given how the spectral density of shot noise can be used to obtain charge quantum in mesoscopic devices

[en] The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of all eigenvalues, for medium matrix sizes, are described with a good precision by nearly normal distributions.

[en] We examine the mathematical and physical significance of the spectral density σ(ω) introduced by Ford [Phys. Rev. D 38, 528 (1988)], defining the contribution of each frequency to the renormalised energy density of a quantum field. Firstly, by considering a simple example, we argue that σ(ω) is well defined, in the sense of being regulator independent, despite an apparently regulator dependent definition. We then suggest that σ(ω) is a spectral distribution, rather than a function, which only produces physically meaningful results when integrated over a sufficiently large range of frequencies and with a high energy smooth enough regulator. Moreover, σ(ω) is seen to be simply the difference between the bare spectral density and the spectral density of the reference background. This interpretation yields a simple ''rule of thumb'' to writing down a (formal) expression for σ(ω) as shown in an explicit example. Finally, by considering an example in which the sign of the Casimir force varies, we show that the spectrum carries no manifest information about this sign; it can only be inferred by integrating σ(ω).

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No abstract available

[en] Complex systems, and in particular random neural networks, are often described by randomly interacting dynamical systems with no specific symmetry. In that context, characterizing the number of relevant directions necessitates fine estimates on the Ginibre ensemble. In this fast track communication, we compute analytically the probability distribution of the number of eigenvalues N_R with modulus greater than R (the index) of a large N × N random matrix in the real or complex Ginibre ensemble. We show that the fraction N_R/N = p has a distribution scaling as exp ( − βN²ψ_R(p)) with β = 2 (respectively β = 1) for the complex (resp. real) Ginibre ensemble. For any p ∈ [0, 1], the equilibrium spectral densities as well as the rate function ψ_R(p) are explicitly derived. This function displays a third order phase transition at the critical (minimum) value p_R^∗=1−R², associated to a phase transition of the Coulomb gas. We deduce that, in the central regime, the fluctuations of the index N_R around its typical value p_R^∗N scale as N^1/3. (fast track communications)

[en] We introduce a novel class of planar random source producing far fields with multi-ring-shaped average intensity patterns by modeling the source degree of coherence, and confirm that such sources are physically genuine. Further, we derive the analytical expressions for the cross-spectral density (CSD) function of the beam-like fields generated by the novel source propagating in free space and in a linear isotropic random medium, and analyze the evolution of the spectral density and the state of coherence. It is shown that at some distance from the source the spectral density of the propagating beam in free space takes on the shape-invariant multi-ring profile, and the number of rings and intensity profiles of the beams can be flexibly adjusted by changing the source parameters. However, in atmospheric turbulence, we find that at sufficiently large distances from the source, the multi-ring profiles are destroyed by the medium, even if it remains such for intermediate distances from the source. (letter)

[en] A review of recent advances in the area of hysteretic nonlinearities driven by di.usion processes is presented. The analysis of these systems is based on the Preisach formalism for the description of hysteresis to represent complex nonlinearities as a weighted superposition of rectangular loops. The mathematical theory of di.usion processes on graphs is then applied to solve problems for stochastically driven hysteresis loops. Closed form expressions for the expected value and spectral density of the output are obtained, and sample computations for these quantities are presented. Because of the universality of the Preisach model, this approach can be used to investigate stochastic aspects in hysteretic systems of various physical origins

[en] We carry out a detailed numerical investigation of stochastic resonance in underdamped systems in the nonperturbative regime. We point out that an important distinction between stochastic resonance in overdamped and underdamped systems lies in the lack of dependence of the amplitude of the noise-averaged trajectory on the noise strength, in the latter case. We provide qualitative explanations for the observed behaviour and show that signatures such as the initial decay and long-time oscillatory behaviour of the temporal correlation function and peaks in the noise and phase averaged power spectral density, clearly indicate the manifestation of resonant behaviour in noisy, underdamped bistable systems in the weak to moderate noise regime

[en] We expose an interesting connection between the distribution of local spectral density of states arising in the theory of disordered systems and the notion of superstatistics introduced by Beck and Cohen and recently incorporated in random matrix theory. The latter represents the matrix-element joint probability density function as an average of the corresponding quantity in the standard random-matrix theory over a distribution of level densities. We show that this distribution is in reasonable agreement with the numerical calculation for a disordered wire, which suggests to use the results of theory of disordered conductors in estimating the parameter distribution of the superstatistical random-matrix ensemble