Infinitely-many absorbing-state nonequilibrium phase transitions

We present a general field-theoretic strategy to analyze three connected families of continuous phase transitions which occur in nonequilibrium steady-states. We focus on transitions taking place between an active state and one absorbing state, when there exist an infinite number of such absorbing states. In such transitions the order parameter is coupled to an auxiliary field. Three situations arise according to whether the auxiliary field is diffusive and conserved, static and conserved, or finally static and not conserved.Comment: 7 pages, 2 .eps figures. To appear in the Brazilian Journal of Physics (2003

Universality class of nonequilibrium phase transitions with infinitely many-absorbing-states

We consider systems whose steady-states exhibit a nonequilibrium phase transition from an active state to one -among an infinite number- absorbing state, as some control parameter is varied across a threshold value. The pair contact process, stochastic fixed-energy sandpiles, activated random walks and many other cellular automata or reaction-diffusion processes are covered by our analysis. We argue that the upper critical dimension below which anomalous fluctuation driven scaling appears is d_c=6, in contrast to a widespread belief (see Dickman cond-mat 0110043 for an overview). We provide the exponents governing the critical behavior close to or at the transition point to first order in a 6-d expansion.Comment: 4 pages, to appear in the Physical Review Letter

Building a path-integral calculus: a covariant discretization approach

Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path integrals have pervaded all areas of physics where fluctuation effects, quantum and/or thermal, are of paramount importance. Their appeal is based on the fact that one converts a problem formulated in terms of operators into one of sampling classical paths with a given weight. Path integrals are the mirror image of our conventional Riemann integrals, with functions replacing the real numbers one usually sums over. However, unlike conventional integrals, path integration suffers a serious drawback: in general, one cannot make non-linear changes of variables without committing an error of some sort. Thus, no path-integral based calculus is possible. Here we identify which are the deep mathematical reasons causing this important caveat, and we come up with cures for systems described by one degree of freedom. Our main result is a construction of path integration free of this longstanding problem, through a direct time-discretization procedure.Comment: 22 pages, 2 figures, 1 table. Typos correcte

Fluctuation-response relations for nonequilibrium diffusions with memory

Strong interaction with other particles or feedback from the medium on a Brownian particle entail memory effects in the effective dynamics. We discuss the extension of the fluctuation-dissipation theorem to nonequilibrium Langevin systems with memory. An important application is to the extension of the Sutherland-Einstein relation between diffusion and mobility. Nonequilibrium corrections include the time-correlation between the dynamical activity and the velocity of the particle, which in turn leads to information about the correlations between the driving force and the particle's displacement

Levy-flight spreading of epidemic processes leading to percolating clusters

We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical point, to directed and isotropic percolation respectively, we consider long-range infections with a probability distribution decaying in d dimensions with the distance as 1/R^{d+\sigma}. By means of Wilson's momentum shell renormalization-group recursion relations, the critical exponents characterizing the growing fractal clusters are calculated to first order in an \epsilon-expansion. It is shown that the long-range critical behavior changes continuously to its short-range counterpart for a decay exponent of the infection \sigma =\sigma_c>2.Comment: 9 pages ReVTeX, 2 postscript figures included, submitted to Eur. Phys. J.

Fluctuations of power injection in randomly driven granular gases

We investigate the large deviation function pi(w) for the fluctuations of the power W(t)=w t, integrated over a time t, injected by a homogeneous random driving into a granular gas, in the infinite time limit. Starting from a generalized Liouville equation we obtain an equation for the generating function of the cumulants mu(lambda) which appears as a generalization of the inelastic Boltzmann equation and has a clear physical interpretation. Reasonable assumptions are used to obtain mu(lambda) in a closed analytical form. A Legendre transform is sufficient to get the large deviation function pi(w). Our main result, apart from an estimate of all the cumulants of W(t) at large times t, is that pi(w) has no negative branch. This immediately results in the failure of the Gallavotti-Cohen Fluctuation Relation (GCFR), that in previous studies had been suggested to be valid for injected power in driven granular gases. We also present numerical results, in order to discuss the finite time behavior of the fluctuations of W(t). We discover that their probability density function converges extremely slowly to its asymptotic scaling form: the third cumulant saturates after a characteristic time larger than 50 mean free times and the higher order cumulants evolve even slower. The asymptotic value is in good agreement with our theory. Remarkably, a numerical check of the GCFR is feasible only at small times, since negative events disappear at larger times. At such small times this check leads to the misleading conclusion that GCFR is satisfied for pi(w). We offer an explanation for this remarkable apparent verification. In the inelastic Maxwell model, where a better statistics can be achieved, we are able to numerically observe the failure of GCFR.Comment: 23 pages, 15 figure

Injected power and entropy flow in a heated granular gas

Our interest goes to the power injected in a heated granular gas and to the possibility to interpret it in terms of entropy flow. We numerically determine the distribution of the injected power by means of Monte-Carlo simulations. Then, we provide a kinetic theory approach to the computation of such a distribution function. Finally, after showing why the injected power does not satisfy a Fluctuation Relation a la Gallavotti-Cohen, we put forward a new quantity which does fulfill such a relation, and is not only applicable in a variety of frameworks outside the granular world, but also experimentally accessible.Comment: accepted in Europhys. Let

Power injected in a granular gas

A granular gas may be modeled as a set of hard-spheres undergoing inelastic collisions; its microscopic dynamics is thus strongly irreversible. As pointed out in several experimental works bearing on turbulent flows or granular materials, the power injected in a dissipative system to sustain a steady-state over an asymptotically large time window is a central observable. We describe an analytic approach allowing us to determine the full distribution of the power injected in a granular gas within a steady-state resulting from subjecting each particle independently either to a random force (stochastic thermostat) or to a deterministic force proportional to its velocity (Gaussian thermostat). We provide an analysis of our results in the light of the relevance, for other types of systems, of the injected power to fluctuation relations.Comment: 9 pages, 4 figures. Contribution to Proceedings of "Work, Dissipation, and Fluctuations in Nonequilibrium Physics", Brussels, 200