Transitional effects of a pension system change in Spain

This paper studies the output effects, transition costs and the change in pension benefits derived from the substitution of the current unfunded pension system by a fully funded pension system financed through mandatory savings.These effects are estimated by using reduced versions of the neoclassical and endogenous growth frameworks. Because of the greater capital accumulation during the transition phase, final output increases by 23,6% (neoclassicalframework); and a 24,5-31,5% (endogenous growth framework). The initial revenue loss for the government would represent a 4,8% of the GDP, raising very slowly during the transition period. Given the new growth rates, rates of return ofphysical capital, and financial intermediation costs, we have that the capitalization pension benefits obtained by all 30-contribution-year worker would be more than twice than those that guarantee the financial sustainability of thepublic pension system

Relaxation times of non-Markovian processes

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

Fluctuations in domain growth: Ginzburg-Landau equations with multiplicative noise

Ginzburg-Landau equations with multiplicative noise are considered, to study the effects of fluctuations in domain growth. The equations are derived from a coarse-grained methodology and expressions for the resulting concentration-dependent diffusion coefficients are proposed. The multiplicative noise gives contributions to the Cahn-Hilliard linear-stability analysis. In particular, it introduces a delay in the domain-growth dynamics.

Front and domain growth in the presence of gravity

Front and domain growth of a binary mixture in the presence of a gravitational field is studied. The interplay of bulk- and surface-diffusion mechanisms is analyzed. An equation for the evolution of interfaces is derived from a time-dependent Ginzburg-Landau equation with a concentration-dependent diffusion coefficient. Scaling arguments on this equation give the exponents of a power-law growth. Numerical integrations of the Ginzburg-Landau equation corroborate the theoretical analysis.

Relaxation time of processes driven by multiplicative noise

We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.

External dichotomous noise: The problem of the mean-first-passage time

A retarded backward equation for a non-Markovian process induced by dichotomous noise (the random telegraphic signal) is deduced. The mean-first-passage time of this process is exactly obtained. The Gaussian white noise and the white shot noise limits are studied. Explicit physical results in first approximation are evaluated.

Higher-order colored-noise effects in multivariable systems

We extend the partial resummation technique of Fokker-Planck terms for multivariable stochastic differential equations with colored noise. As an example, a model system of a Brownian particle with colored noise is studied. We prove that the asymmetric behavior found in analog simulations is due to higher-order terms which are left out in that technique. On the contrary, the systematic ¿-expansion approach can explain the analog results.

Escape over a potential barrier driven by colored noise: Large but finite correlation times

The recent theory of Tsironis and Grigolini for the mean first-passage time from one metastable state to another of a bistable potential for long correlation times of the noise is extended to large but finite correlation times.

Relaxation from a marginal state in optical bistability

Characteristic decay times for relaxation close to the marginal point of optical bistability are studied. A model-independent formula for the decay time is given which interpolates between Kramers time for activated decay and a deterministic relaxation time. This formula gives the decay time as a universal scaling function of the parameter which measures deviation from marginality. The standard deviation of the first-passage-time distribution is found to vary linearly with the decay time, close to marginality, with a slope independent of the noise intensity. Our results are substantiated by numerical simulations and their experimental relevance is pointed out.

Transient and preparation colored-noise effects: The nonlinear relaxation-time approach

We develop a singular perturbation approach to the problem of the calculation of a characteristic time (the nonlinear relaxation time) for non-Markovian processes driven by Gaussian colored noise with small correlation time. Transient and initial preparation effects are discussed and explicit results for prototype situations are obtained. New effects on the relaxation of unstable states are predicted. The approach is compared with previous techniques.

Decay of unstable states in the presence of colored noise and random initial conditions. I. Theory of nonlinear relaxation times

The general theory of nonlinear relaxation times is developed for the case of Gaussian colored noise. General expressions are obtained and applied to the study of the characteristic decay time of unstable states in different situations, including white and colored noise, with emphasis on the distributed initial conditions. Universal effects of the coupling between colored noise and random initial conditions are predicted.

Turn-on-time statistics of modulated lasers subjected to resonant weak optical feedback

We present analytical calculations of the turn-on-time probability distribution of intensity-modulated lasers under resonant weak optical feedback. Under resonant conditions, the external cavity round-trip time is taken to be equal to the modulation period. The probability distribution of the solitary laser results are modified to give reduced values of the mean turn-on-time and its variance. Numerical simulations have been carried out showing good agreement with the analytical results.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Generator of ultrashort optical pulses for time division multiplexing

The performance of a device based on modified injection-locking techniques is studied by means of numerical simulations. The device incorporates master and slave configurations, each one with a DFB laser and an electroabsortion modulator (EAM). This arrangement allows the generation of high peak power, narrow optical pulses according to a periodic or pseudorandom bit stream provided by a current signal generator. The device is able to considerably increase the modulation bandwidth of free-running gain-switched semiconductor lasers using multiplexing in the time domain. Opportunities for integration in small packages or single chips are discussed.