The dynamical structure factor in topologically disordered systems

A computation of the dynamical structure factor of topologically disordered systems, where the disorder can be described in terms of euclidean random matrices, is presented. Among others, structural glasses and supercooled liquids belong to that class of systems. The computation describes their relevant spectral features in the region of the high frequency sound. The analytical results are tested with numerical simulations and are found to be in very good agreement with them. Our results may explain the findings of inelastic X-ray scattering experiments in various glassy systems.Comment: Version to be published in J. Chem. Phy

Statistics of non-linear stochastic dynamical systems under L\'evy noises by a convolution quadrature approach

This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficient way, independently from the kind of white noise; 2) The particular form of Wiener-Hopf integral transform and its numerical evaluation, both introduced in this study, are generalizations of fractional integro-differential operators of potential type and Gr\"unwald-Letnikov fractional derivatives, respectively.Comment: 20 pages, 5 figure

Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions

This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws.Comment: LaTeX; 40 pages; review pape

Ground state of many-body lattice systems via a central limit theorem

We review a novel approach to evaluate the ground-state properties of many-body lattice systems based on an exact probabilistic representation of the dynamics and its long time approximation via a central limit theorem. The choice of the asymptotic density probability used in the calculation is discussed in detail.Comment: 9 pages, contribution to the proceedings of 12th International Conference on Recent Progress in Many-Body Theories, Santa Fe, New Mexico, August 23-27, 200

Data Assimilation using a GPU Accelerated Path Integral Monte Carlo Approach

The answers to data assimilation questions can be expressed as path integrals over all possible state and parameter histories. We show how these path integrals can be evaluated numerically using a Markov Chain Monte Carlo method designed to run in parallel on a Graphics Processing Unit (GPU). We demonstrate the application of the method to an example with a transmembrane voltage time series of a simulated neuron as an input, and using a Hodgkin-Huxley neuron model. By taking advantage of GPU computing, we gain a parallel speedup factor of up to about 300, compared to an equivalent serial computation on a CPU, with performance increasing as the length of the observation time used for data assimilation increases.Comment: 5 figures, submitted to Journal of Computational Physic

Net-baryon multiplicity distribution consistent with lattice QCD

We determine the net-baryon multiplicity distribution which reproduces all cumulants measured so far by lattice QCD. We present the dependence on the volume and temperature of this distribution. We find that for temperatures and volumes encountered in heavy ion reactions, the multiplicity distribution is very close to the Skellam distribution, making the experimental determination of it rather challenging. We further provide estimates for the statistics required to measure cumulants of the net-baryon and net-proton distributions.Comment: 13 pages, 6 figures; Extended version. Now include statistics estimate for RHIC and LHC based on delta metho