Fluctuation Dissipation Relation for a Langevin Model with Multiplicative Noise

A random multiplicative process with additive noise is described by a Langevin equation. We show that the fluctuation-dissipation relation is satisfied in the Langevin model, if the noise strength is not so strong.Comment: 11 pages, 6 figures, other comment

Damage Spreading in the Ising Model

We present two new results regarding damage spreading in ferromagnetic Ising models. First, we show that a damage spreading transition can occur in an Ising chain that evolves in contact with a thermal reservoir. Damage heals at low temperature and spreads for high T. The dynamic rules for the system's evolution for which such a transition is observed are as legitimate as the conventional rules (Glauber, Metropolis, heat bath). Our second result is that such transitions are not always in the directed percolation universality class.Comment: 5 pages, RevTeX, revised and extended version, including 3 postscript figure

Lorentz-CPT violation, radiative corrections and finite temperature

In this work we investigate the radiatively induced Chern-Simons-like terms in four-dimensions at zero and finite temperature. We use the approach of rationalizing the fermion propagator up to the leading order in the CPT-violating coupling $b_\mu$. In this approach, we have shown that although the coefficient of Chern-Simons term can be found unambiguously in different regularization schemes at zero or finite temperature, it remains undetermined. We observe a correspondence among results obtained at finite and zero temperature.Comment: To appear in JHEP, 10 pages, 1 eps figure, minor changes and references adde

Nonextensive Thermostatistics and the H-Theorem

The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the ``molecular chaos hypothesis". For $q>0$, the $q$-transport equation satisfies an $H$-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' $q$-nonextensive velocity distribution.Comment: 4 pages, no figures, corrected some typo

Damage spreading for one-dimensional, non-equilibrium models with parity conserving phase transitions

The damage spreading (DS) transitions of two one-dimensional stochastic cellular automata suggested by Grassberger (A and B) and the kinetic Ising model of Menyh\'ard (NEKIM) have been investigated on the level of kinks and spins. On the level of spins the parity conservation is not satisfied and therefore studying these models provides a convenient tool to understand the dependence of DS properties on symmetries. For the model B the critical point and the DS transition point is well separated and directed percolation damage spreading transition universality was found for spin damage as well as for kink damage in spite of the conservation of damage variables modulo 2 in the latter case. For the A stochastic cellular automaton, and the NEKIM model the two transition points coincide with drastic effects on the damage of spin and kink variables showing different time dependent behaviours. While the kink DS transition is continuous and shows regular PC class universality, the spin damage exhibits a discontinuous phase transition with compact clusters and PC like dynamical scaling ($\eta^,$), ($\delta_s$) and ($z_s$) exponents whereas the static exponents determined by FSS are consistent with that of the spins of the NEKIM model at the PC transition point. The generalised hyper-scaling law is satisfied.Comment: 11 pages, 20 figures embedded in the text, minor changes in the text, a new table and new references are adde

Nonextensivity and multifractality in low-dimensional dissipative systems

Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed in the generalized statistics recently introduced by one of us (C.T.) and characterized by the entropic index $q$. We show that general scaling arguments imply that $1/(1-q) = 1/\alpha_{min}-1/\alpha_{max}$, where $\alpha_{min}$ and $\alpha_{max}$ are the extremes of the multifractal singularity spectrum $f(\alpha)$ of the attractor. This relation is numerically checked to hold in standard one-dimensional dissipative maps. The above result sheds light on a long-standing puzzle concerning the relation between the entropic index $q$ and the underlying microscopic dynamics.Comment: 12 pages, TeX, 4 ps figure

Noncommutative massive Thirring model in three-dimensional spacetime

We evaluate the noncommutative Chern-Simons action induced by fermions interacting with an Abelian gauge field in a noncommutative massive Thirring model in (2+1)-dimensional spacetime. This calculation is performed in the Dirac and Majorana representations. We observe that in Majorana representation when $\theta$ goes to zero we do not have induced Chern-Simons term in the dimensional regularization scheme.Comment: Accepted to Phys. Rev. D; 9 pages, Revtex4, no figures, references added, minor improvements, Eq.31 correcte

Nonextensive approach to decoherence in quantum mechanics

We propose a nonextensive generalization (q parametrized) of the von Neumann equation for the density operator. Our model naturally leads to the phenomenon of decoherence, and unitary evolution is recovered in the limit of q -> 1. The resulting evolution yields a nonexponential decay for quantum coherences, fact that might be attributed to nonextensivity. We discuss, as an example, the loss of coherence observed in trapped ions.Comment: 4 pages, RevTeX, 1 figure We have corrected a problem with the figures' file as well as a few misprint