Stochastic resonance and heat fluctuations in a driven double-well system

We study a periodically driven (symmetric as well as asymmetric) double-well potential system at finite temperature. We show that mean heat loss by the system to the environment (bath) per period of the applied field is a good quantifier of stochastic resonance. It is found that the heat fluctuations over a single period are always larger than the work fluctuations. The observed distributions of work and heat exhibit pronounced asymmetry near resonance. The heat loss over a large number of periods satisfies the conventional steady-state fluctuation theorem.     

Dynamical stability of systems with long-range interactions: application of the Nyquist method to the HMF model

We apply the Nyquist method to the Hamiltonian mean field (HMF) model in order to settle the linear dynamical stability of a spatially homogeneous distribution function with respect to the Vlasov equation. We consider the case of Maxwell (isothermal) and Tsallis (polytropic) distributions and show that the system is stable above a critical kinetic temperature T_c and unstable below it. Then, we consider a symmetric double-humped distribution, made of the superposition of two decentered Maxwellians, and show the existence of a re-entrant phase in the stability diagram. When we consider an asymmetric double-humped distribution, the re-entrant phase disappears above a critical value of the asymmetry factor Δ > 1.09. We also consider the HMF model with a repulsive interaction. In that case, single-humped distributions are always stable. For asymmetric double-humped distributions, there is a re-entrant phase for 1 ≤ Δ < 25.6, a double re-entrant phase for 25.6 < Δ < 43.9 and no re-entrant phase for Δ > 43.9. Finally, we extend our results to arbitrary potentials of interaction and mention the connexion between the HMF model, Coulombian plasmas and gravitational systems. We discuss the relation between linear dynamical stability and formal nonlinear dynamical stability and show their equivalence for spatially homogeneous distributions. We also provide a criterion of dynamical stability for spatially inhomogeneous systems.     

Can a few fanatics influence the opinion of a large segment of a society?

Models that provide insight into how extreme positions regarding any social phenomenon may spread in a society or at the global scale are of great current interest. A realistic model must account for the fact that globalization, internet, and other means of mass communications have given rise to scale-free networks of interactions between people. We propose a novel model which takes into account the nature of the interactions network, and provides some key insights into this phenomenon. These include, (1) the existence of a fundamental difference between a hierarchical network whereby people are influenced by those that are higher in the hierarchy but not by those below them, and a symmetrical network where person-on-person influence works mutually, and (2) that a few “fanatics” can influence a large fraction of the population either temporarily (in the hierarchical networks) or permanently (in symmetrical networks). Even if the “fanatics” disappear, the population may still remain susceptible to the positions originally advocated by them. The model is, however, general and applicable to any phenomenon for which there is a degree of enthusiasm or susceptibility to in the population.     

Escape of Brownian particles in an asymmetric bistable sawtooth potential driven by cross-correlated noises

The relative escape rate (RER) for Brownian particles in an asymmetric bistable sawtooth potential driven by cross correlations between multiplicative white noise and additive white noise is studied. A new expression of the mean first-passage time is derived under the condition of piecewise linear potentials and discontinuous diffusion function. Based on the results of RER numerically calculated, it is found that (i) under positively correlated noises action (i.e. λ > 0, and λ is the correlation strength), the escape rate exhibits the suppression platform as the intensity of multiplicative noise varies. The effect of suppression becomes more pronounced with the growth of height of the deterministic potential barrier for transition, and with the increase of λ. However, for the case of uncorrelated noises (λ = 0) and of negatively correlated noises (λ < 0), the suppression platform disappears. (ii) The positive correlation between noises amplifies the change of the escape rate with the height of barrier for transition, while the negative correlation between noises suppresses this change. Received 20 November 2002 / Received in final form 19 October 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: kmdcmei@public.km.yn.cn     

Power injected in dissipative systems and the fluctuation theorem

We consider three examples of dissipative dynamical systems involving many degrees of freedom, driven far from equilibrium by a constant or time dependent forcing. We study the statistical properties of the injected and dissipated power as well as the fluctuations of the total energy of these systems. The three systems under consideration are: a shell model of turbulence, a gas of hard spheres colliding inelastically and excited by a vibrating piston, and a Burridge-Knopoff spring-block model. Although they involve different types of forcing and dissipation, we show that the statistics of the injected power obey the “fluctuation theorem" demonstrated in the case of time reversible dissipative systems maintained at constant total energy, or in the case of some stochastic processes. Although this may be only a consequence of the theory of large deviations, this allows a possible definition of “temperature" for a dissipative system out of equilibrium. We consider how this “temperature" scales with the energy and the number of degrees of freedom in the different systems under consideration. Received 26 June 2000 and Received in final form 24 October 2000     

Open dynamic behaviour of financial markets

Open dynamic behaviour of financial markets with internal interactions between agents and with external “fields” from other systems are investigated using the approach of Grossman and Stiglitz for inefficient markets, and Keynes for interference of the market using physics of finance (referred to hereafter as phynance). The simulation results indicate that the NYSE data analyzed in Plerou, V. et al., Nature 421, 130 (2003) can be fitted by an equation of order parameter Φ and local deviation R of type: -(R+0.03) Φ+ 0.6 Φ³ + 0.02 = 0, which is shown to be in remarkable agreement with Plerou's data.     

Steady-states and kinetics of ordering in bus-route models: connection with the Nagel-Schreckenberg model

A Bus Route Model (BRM) can be defined on a one-dimensional lattice, where buses are represented by “particles” that are driven forward from one site to the next with each site representing a bus stop. We replace the random sequential updating rules in an earlier BRM by parallel updating rules. In order to elucidate the connection between the BRM with parallel updating (BRMPU) and the Nagel-Schreckenberg (NaSch) model, we propose two alternative extensions of the NaSch model with space-/time-dependent hopping rates. Approximating the BRMPU as a generalization of the NaSch model, we calculate analytically the steady-state distribution of the time headways (TH) which are defined as the time intervals between the departures (or arrivals) of two successive particles (i.e., buses) recorded by a detector placed at a fixed site (i.e., bus stop) on the model route. We compare these TH distributions with the corresponding results of our computer simulations of the BRMPU, as well as with the data from the simulation of the two extended NaSch models. We also investigate interesting kinetic properties exhibited by the BRMPU during its time evolution from random initial states towards its steady-states. Received 16 December 1999     

Phase transitions induced by thermal fluctuations

The present study generalizes the model of extended stochastic systems with a field-dependent kinetic coefficient [M. Ibanes, J. Garcia-Ojalvo, R. Toral, J.M. Sancho, Phys. Rev. Lett. 87, 020601 (2001)] to systems with symmetric and asymmetric bistable potentials. It is found that in systems with a relaxational flow and a symmetric local potential, reentrant phase transitions can be observed. In the case of an asymmetric local potential, a hysteresis-like behaviour in the order parameter appears. It is shown that such phase transitions can be controlled by the constant that governs relaxation flow, noise intensity and spatial coupling intensity.     

Curious behaviour of the diffusion coefficient and friction force for the strongly inhomogeneous HMF model

We present first elements of kinetic theory appropriate to the inhomogeneous phase of the Hamiltonian Mean Field (HMF) model. In particular, we investigate the case of strongly inhomogeneous distributions for T→0 and exhibit curious behaviour of the force auto-correlation function and friction coefficient. The temporal correlation function of the force has an oscillatory behaviour which averages to zero over a period. By contrast, the effects of friction accumulate with time and the friction coefficient does not satisfy the Einstein relation. On the contrary, it presents the peculiarity to increase linearly with time. Motivated by this result, we provide analytical solutions of a simplified kinetic equation with a time dependent friction. Analogies with self-gravitating systems and other systems with long-range interactions are also mentioned.     

Autoionization of an ultracold Rydberg gas through resonant dipole coupling

We investigate a possible mechanism for the autoionization of ultracold Rydberg gases, based on the resonant coupling of Rydberg pair states to the ionization continuum. Unlike an atomic collision where the wave functions begin to overlap, the mechanism considered here involves only the long-range dipole interaction and is in principle possible in a static system. It is related to the process of intermolecular Coulombic decay (ICD). In addition, we include the interaction-induced motion of the atoms and the effect of multi-particle systems in this work. We find that the probability for this ionization mechanism can be increased in many-particle systems featuring attractive or repulsive van der Waals interactions. However, the rates for ionization through resonant dipole coupling are very low. It is thus unlikely that this process contributes to the autoionization of Rydberg gases in the form presented here, but it may still act as a trigger for secondary ionization processes. As our picture involves only binary interactions, it remains to be investigated if collective effects of an ensemble of atoms can significantly influence the ionization probability. Nevertheless our calculations may serve as a starting point for the investigation of more complex systems, such as the coupling of many pair states proposed in [P.J. Tanner et al., Phys. Rev. Lett. 100, 043002 (2008)].     

Exact Bures probabilities that two quantum bits are classically correlated

In previous studies, we have explored the ansatz that the volume elements of the Bures metrics over quantum systems might serve as prior distributions, in analogy with the (classical) Bayesian role of the volume elements (“Jeffreys' priors”) of Fisher information metrics. Continuing this work, we obtain exact Bures prior probabilities that the members of certain low-dimensional subsets of the fifteen-dimensional convex set of density matrices are separable or classically correlated. The main analytical tools employed are symbolic integration and a formula of Dittmann (J. Phys. A 32, 2663 (1999)) for Bures metric tensors. This study complements an earlier one (J. Phys. A 32, 5261 (1999)) in which numerical (randomization) - but not integration - methods were used to estimate Bures separability probabilities for unrestricted and density matrices. The exact values adduced here for pairs of quantum bits (qubits), typically, well exceed the estimate () there, but this disparity may be attributable to our focus on special low-dimensional subsets. Quite remarkably, for the q= 1 and states inferred using the principle of maximum nonadditive (Tsallis) entropy, the Bures probabilities of separability are both equal to . For the Werner qubit-qutrit and qutrit-qutrit states, the probabilities are vanishingly small, while in the qubit-qubit case it is . Received 10 December 1999 and Received in final form 24 February 2000     

Dynamic renormalization-group analysis of the d+1 dimensional Kuramoto-Sivashinsky equation with both conservative and nonconservative noises

The long-wavelength properties of the (d + 1)-dimensional Kuramoto-Sivashinsky (KS) equation with both conservative and nonconservative noises are investigated by use of the dynamic renormalization-group (DRG) theory. The dynamic exponent z and roughness exponent α are calculated for substrate dimensions d = 1 and d = 2, respectively. In the case of d = 1, we arrive at the critical exponents z = 1.5 and α = 0.5 , which are consistent with the results obtained by Ueno et al. in the discussion of the same noisy KS equation in 1+1 dimensions [Phys. Rev. E 71, 046138 (2005)] and are believed to be identical with the dynamic scaling of the Kardar-Parisi-Zhang (KPZ) in 1+1 dimensions. In the case of d = 2, we find a fixed point with the dynamic exponents z = 2.866 and α = -0.866 , which show that, as in the 1 + 1 dimensions situation, the existence of the conservative noise in 2 + 1 or higher dimensional KS equation can also lead to new fixed points with different dynamic scaling exponents. In addition, since a higher order approximation is adopted, our calculations in this paper have improved the results obtained previously by Cuerno and Lauritsen [Phys. Rev. E 52, 4853 (1995)] in the DRG analysis of the noisy KS equation, where the conservative noise is not taken into account.     

Active Brownian motion models and applications to ratchets

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.     

Short-range plasma model for intermediate spectral statistics

We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the critical point of the Anderson metal-insulator transition in disordered systems and in certain dynamical systems. The model emerges from Dysons one-dimensional gas corresponding to the eigenvalue distribution of the classical random matrix ensembles by restricting the logarithmic pair interaction to a finite number k of nearest neighbors. We calculate analytically the spacing distributions and the two-level statistics. In particular we show that the number variance has the asymptotic form Σ²(L) ∼χL for large L and the nearest-neighbor distribution decreases exponentially when s→∞, P(s) ∼ exp(- Λs) with Λ = 1/χ = kβ + 1, where β is the inverse temperature of the gas (β = 1, 2 and 4 for the orthogonal, unitary and symplectic symmetry class respectively). In the simplest case of k = β = 1, the model leads to the so-called Semi-Poisson statistics characterized by particular simple correlation functions e.g. P(s) = 4s exp(- 2s). Furthermore we investigate the spectral statistics of several pseudointegrable quantum billiards numerically and compare them to the Semi-Poisson statistics. Received 13 September 2000     

On the optimality of individual entangling-probe attacks against BB84 quantum key distribution

Some MIT researchers [Phys. Rev. A 75, 042327 (2007)] have recently claimed that their implementation of the Slutsky-Brandt attack [Phys. Rev. A 57, 2383 (1998); Phys. Rev. A 71, 042312 (2005)] to the BB84 quantum-key-distribution (QKD) protocol puts the security of this protocol “to the test” by simulating “the most powerful individual-photon attack” [Phys. Rev. A 73, 012315 (2006)]. A related unfortunate news feature by a scientific journal [G. Brumfiel, Quantum cryptography is hacked, News @ Nature (april 2007); Nature 447, 372 (2007)] has spurred some concern in the QKD community and among the general public by misinterpreting the implications of this work. The present article proves the existence of a stronger individual attack on QKD protocols with encrypted error correction, for which tight bounds are shown, and clarifies why the claims of the news feature incorrectly suggest a contradiction with the established “old-style” theory of BB84 individual attacks. The full implementation of a quantum cryptographic protocol includes a reconciliation and a privacy-amplification stage, whose choice alters in general both the maximum extractable secret and the optimal eavesdropping attack. The authors of [Phys. Rev. A 75, 042327 (2007)] are concerned only with the error-free part of the so-called sifted string, and do not consider faulty bits, which, in the version of their protocol, are discarded. When using the provably superior reconciliation approach of encrypted error correction (instead of error discard), the Slutsky-Brandt attack is no more optimal and does not “threaten” the security bound derived by Lütkenhaus [Phys. Rev. A 59, 3301 (1999)]. It is shown that the method of Slutsky and collaborators [Phys. Rev. A 57, 2383 (1998)] can be adapted to reconciliation with error correction, and that the optimal entangling probe can be explicitly found. Moreover, this attack fills Lütkenhaus bound, proving that it is tight (a fact which was not previously known).     

Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane

We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented by D. Lacoste, M. Cosentino Lagomarsino, and J.F. Joanny (EPL 77, 18006 (2007)), by providing a physical explanation for a destabilizing term proportional to k _⊥ ³ in the fluctuation spectrum, which we relate to a nonlinear (E²) electrokinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives the flow along the field axis toward surface protrusions; in contrast, we predict “reverse” ICEO flows around driven membranes, due to curvature-induced tangential fields within a nonequilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.     

Microscopic study reveals the singular origins of growth

Anderson [Science 177, 293 (1972)] proposed the concept of complexity in order to describe the emergence and growth of macroscopic collective patterns out of the simple interactions of many microscopic agents. In the physical sciences this paradigm was implemented systematically and confirmed repeatedly by successful confrontation with reality. In the social sciences however, the possibilities to stage experiments to validate it are limited. During the 90's a series of dramatic political and economic events have provided the opportunity to do so. We exploit the resulting empirical evidence to validate a simple agent based alternative to the classical logistic dynamics. The post-liberalization empirical data from Poland confirm the theoretical prediction that the dynamics is dominated by singular rare events which insure the resilience and adaptability of the system. We have shown that growth is led by few singular “growth centers" (Fig. 1), that initially developed at a tremendous rate (Fig. 3), followed by a diffusion process to the rest of the country and leading to a positive growth rate uniform across the counties. In addition to the interdisciplinary unifying potential of our generic formal approach, the present work reveals the strong causal ties between the “softer" social conditions and their “hard" economic consequences.     

Detecting and quantifying temporal correlations in stochastic resonance via information theory measures

We show that Information Theory quantifiers are suitable tools for detecting and for quantifying noise-induced temporal correlations in stochastic resonance phenomena. We use the Bandt & Pompe (BP) method [Phys. Rev. Lett. 88, 174102 (2002)] to define a probability distribution, P, that fully characterizes temporal correlations. The BP method is based on a comparison of neighboring values, and here is applied to the temporal sequence of residence-time intervals generated by the paradigmatic model of a Brownian particle in a sinusoidally modulated bistable potential. The probability distribution P generated via the BP method has associated a normalized Shannon entropy, H[P], and a statistical complexity measure, C[P], which is defined as proposed by Rosso et al. [Phys. Rev. Lett. 99, 154102 (2007)]. The statistical complexity quantifies not only randomness but also the presence of correlational structures, the two extreme circumstances of maximum knowledge (“perfect order") and maximum ignorance (“complete randomness") being regarded an “trivial", and in consequence, having complexity C = 0. We show that both, H and C, display resonant features as a function of the noise intensity, i.e., for an optimal level of noise the entropy displays a minimum and the complexity, a maximum. This resonant behavior indicates noise-enhanced temporal correlations in the sequence of residence-time intervals. The methodology proposed here has great potential for the precise detection of subtle signatures of noise-induced temporal correlations in real-world complex signals.