Metastable behavior of stochastic dynamics: A pathwise approach

In this paper a new approach to metastability for stochastic dynamics is proposed. The basic idea is to study the statistics of each path, performing time averages along the evolution. Metastability would be characterized by the fact that the process of these time averages converges, under a suitable rescaling, to a measure valued Markov jump process. Here this convergence is shown for the Curie-Weiss mean field dynamics and also for a model with spatial structure: Harris contact process.Partially supported by CNPq, Grant No. 301301/79.     

Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.     

Linear stochastic dynamics with nonlinear fractal properties

Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We present a review of applications, highlight the common physical mechanism and summarize the main known results. The distribution and statistical properties of the duration of intermittent bursts are also characterized in detail.     

Stochastic dynamics of two-dimensional infinite-particle systems

The time evolution of an open system of infinitely many two-dimensional classical particles is investigated. Particles are interacting by a singular pair potentialU, and each particle is connected to a heat bath of temperatureT. The heat baths are represented by independent white noise forces and Langevin damping terms. Existence of strong solutions to the corresponding infinite system of stochastic differential equations is proved for initial configurations with a logarithmic order of energy fluctuations. Gibbs states forU at temperatureT are invariant under time evolution.     

Evolutionary dynamics of nationalism and migration

I present a dynamic evolutionary game model to address the relation between nationalism against immigrants and assimilation of the latter into the host country culture. I assume a country composed of two different large polymorphic populations, one of native citizens and the other of immigrants. A native citizen may behave nationalistically or may welcome immigrants. Immigrants may have an interest in learning the host country language or not. Evolution is modeled using replicator dynamics (RD). I also account for the presence of an enclave of immigrants in the host country. In the RD, the latter represents the immigrants’ own population effect, which contribution to fitness is controlled using a parameter ρ$\rho$, 0≤ρ≤1$0\le \rho \le 1$, that represents the enclave size. In line with the empirical literature on migration, the existence of an enclave of immigrants makes assimilation less likely to occur. For large values of ρ$\rho$, complete assimilation may not occur even if immigrants and natives share very close cultures and norms. Government policy regarding nationalism is modeled both exogenously and endogenously. A single or multiple asymptotically stable states exist for all cases studied but one in which the dynamics is similar to that found in the predator–prey model of Lotka–Volterra for competing species.     

A stochastic approach to Wilson loops

Wilson loops exp (i A (x) dx) are investigated in two-dimensional Euclidean space-time. The electromagnetic vector potential A is regarded as a generalized random field given by the stochastic partial differential equation A = F where is a first-order differential operator and F is white noise. We give a rigorous definition of Wilson loops and examine the properties of the N-loop Schwinger functions.     

Percolation analysis of stochastic models of galactic evolution

The stochastic star formation model of galactic evolution can be cast as a problem of directed percolation, the time dimension being that along which the directed bonds exist. We study various aspects of this percolation, those of general interest for the percolation phase transition and those of particular importance for the astrophysical application. Both analytical calculations and computer simulations are provided and the results compared. Among the properties are: value of the percolation threshold, critical indices, percolation probability (star density) near and away from the critical point, local density, cluster sizes, effects of rotation (for disk galaxy models) on the percolation threshold. Astrophysical consequences of some of these properties are discussed, in particular the way in which general phase transition behavior contributes to spiral arm morphology. We look at 1 (space) + 1 (time), 2 + 1 and + 1 dimensions, the 2 + 1 case being of interest for disk galaxies.     

A stochastic model for the dynamics of a classical spin

A stochastic model for the dynamics of a macroscopic or classical spin based on a classical generalized Lagrangian formalism is proposed. The model can be used to describe the evolution of the magnetic moment of superparamagnetic particles. In this sense, it is a generalization of the model proposed by Brown, allowing for fluctuations on the magnitudes of the magnetic moments of the particles. The corresponding covariant Fokker-Planck equation is also obtained.     

Electroless formation of silver nanoaggregates: an experimental and molecular dynamics approach

The ability to manipulate matter to create non-conventional structures is one of the key issues of material science. The understanding of assembling mechanism at the nanoscale allows us to engineer new nanomaterials, with physical properties intimately depending on their structure.

This paper describes new strategies to obtain and characterise metal nanostructures via the combination of a top-down method, such as electron beam lithography, and a bottom-up technique, such as the chemical electroless deposition. We realised silver nanoparticle aggregates within well-defined patterned holes created by electron beam lithography on silicon substrates. The quality characteristics of the nanoaggregates were verified by using scanning electron microscopy and atomic force microscopy imaging. Moreover, we compared the experimental findings to molecular dynamics simulations of nanoparticles growth. We observed a very high dependence of the structure characteristics on the pattern nanowell aspect ratio. We found that high-quality metal nanostructures may be obtained in patterns with well aspect ratio close to one, corresponding to a maximum diameter of 50 nm, a limit above which the fabricated structures become less regular and discontinuous. When regular shapes and sizes are necessary, as in nanophotonics, these results suggest the pattern characteristics to obtain isolated, uniform and reproducible metal nanospheres.     

First passage time for a class of one-dimensional stochastic systems

We consider the time evolution of a class of stochastic systems of finite size with polynomial nearest neighbor transition rates. We obtain analytical expressions for the first passage time (FPT) and its moments. We show that the mean FPT, averaged over a uniform initial distribution, shows a simple asymptotoc behavior with the system size and the parameters of the transition rates.     

A continuous model of human dynamics

Ideas and tools from statistical physics have recently been applied to the investigation of human dynamics. The timing of human activities, in particular, has been studied both experimentally and analytically. Empirical data show that, in many different situations, the time interval separating two consecutive tasks executed by an individual follows a heavy-tailed probability distribution rather than Poisson statistics. To account for this data, human behaviour has been viewed as a decision-based queuing system where individuals select and execute tasks belonging to a finite list of items as an increasing function of a task priority parameter. It is then possible to obtain analytically the empirical result P(τ)∼1/τ, where P(τ) is the waiting time probability distribution.Here a continuous model of human dynamics is introduced using instead an infinite queuing list. In contrast with the results obtained by other models in the finite case we find a waiting time distribution explicitly depending on the priority distribution density function ρ. The power-law scaling P(τ)∼1/τ is then recovered when ρ is exponentially distributed.     

Macroscopic Lyapunov functions for separable stochastic neural networks with detailed balance

We derive macroscopic Lyapunov functions for large, long-range, Ising-spin neural networks with separable symmetric interactions, which evolve in time according to local field alignment. We generalize existing constructions, which correspond todeterministic (zero-temperature) evolution and to specific choices of the interaction structure, to the case ofstochastic evolution and arbitrary separable interaction matrices, for both parallel and sequential spin updating. We find a direct relation between the form of the Lyapunov functions (which describe dynamical processes) and the saddle-point integration that results from performing equilibrium statistical mechanical studies of the present type of model.     

Non-Markovian random unitary qubit dynamics

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates.     

Coupling induced logical stochastic resonance

In this work we will demonstrate the following result: when we have two coupled bistable sub-systems, each driven separately by an external logic input signal, the coupled system yields outputs that can be mapped to specific logic gate operations in a robust manner, in an optimal window of noise. So, though the individual systems receive only one logic input each, due to the interplay of coupling, nonlinearity and noise, they cooperatively respond to give a logic output that is a function of both inputs. Thus the emergent collective response of the system, due to the inherent coupling, in the presence of a noise floor, maps consistently to that of logic outputs of the two inputs, a phenomenon we term coupling induced Logical Stochastic Resonance. Lastly, we demonstrate our idea in proof of principle circuit experiments.     

A sigma-model approach to glassy dynamics

In this contribution we review recent progress in understanding fluctuations in the aging process of macroscopic systems, and we propose further tests of these ideas. We discuss how the emergence of a symmetry in aging systems, global timereparametrization invariance, could be responsible for the observed ‘universal’ behavior of local and mesoscopic non-equilibrium fluctuations. We discuss (i) the two-time scaling and functional form of the distribution of local correlations and responses; (ii) the scaling of multi-time correlations and susceptibilities; (iii) how the above can be derived from a random surface effective action; (iv) the behavior of a diverging two-time dependent correlation length; (v) how these ideas apply to off-lattice particle systems.