Correlation of eigenstates in the critical regime of quantum Hall systems

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, $\alpha_0\approx 2.28$, gives an almost complete characterization of the critical behavior of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure

Comment on ``Critical behavior of a two-species reaction-diffusion problem''

In a recent paper, de Freitas et al. [Phys. Rev. E 61, 6330 (2000)] presented simulational results for the critical exponents of the two-species reaction-diffusion system A + B -> 2B and B -> A in dimension d = 1. In particular, the correlation length exponent was found as \nu = 2.21(5) in contradiction to the exact relation \nu = 2/d. In this Comment, the symmetry arguments leading to exact critical exponents for the universality class of this reaction-diffusion system are concisely reconsidered

Mean-field scaling function of the universality class of absorbing phase transitions with a conserved field

We consider two mean-field like models which belong to the universality class of absorbing phase transitions with a conserved field. In both cases we derive analytically the order parameter as function of the control parameter and of an external field conjugated to the order parameter. This allows us to calculate the universal scaling function of the mean-field behavior. The obtained universal function is in perfect agreement with recently obtained numerical data of the corresponding five and six dimensional models, showing that four is the upper critical dimension of this particular universality class.Comment: 8 pages, 2 figures, accepted for publication in J. Phys.

Quine, Ontology, and Physicalism

Quine's views on ontology and naturalism are well-known but rarely considered in tandem. According to my interpretation the connection between them is vital. I read Quine as a global epistemic structuralist. Quine thought we only ever know objects qua solutions to puzzles about significant intersections in observations. Objects are always accessed descriptively, via their roles in our best theory. Quine's Kant lectures contain an early version of epistemic structuralism with uncharacteristic remarks about the mental. Here Quine embraces mitigated anomalous monism, allowing introspection and the availability in principle of full physical descriptions of the perceptual states which get science off the ground. Later versions abandon these ideas. My epistemic-structural interpretation explains why. I argue first-personal introspective access to mental states is incompatible with global epistemic structuralism

Renormalization group of probabilistic cellular automata with one absorbing state

We apply a recently proposed dynamically driven renormalization group scheme to probabilistic cellular automata having one absorbing state. We have found just one unstable fixed point with one relevant direction. In the limit of small transition probability one of the cellular automata reduces to the contact process revealing that the cellular automata are in the same universality class as that process, as expected. Better numerical results are obtained as the approximations for the stationary distribution are improved.Comment: Errors in some formulas have been corrected. Additional material available at http://mestre.if.usp.br/~javie

Crack fronts and damage in glass at the nanometer scale

We have studied the low speed fracture regime for different glassy materials with variable but controlled length scales of heterogeneity in a carefully mastered surrounding atmosphere. By using optical and atomic force microscopy (AFM) techniques we tracked in real-time the crack tip propagation at the nanometer scale on a wide velocity range (mm/s - pm/s and below). The influence of the heterogeneities on this velocity is presented and discussed. Our experiments reveal also -for the first time- that the crack progresses through nucleation, growth and coalescence of nanometric damage cavities within the amorphous phase. This may explain the large fluctuations observed in the crack tip velocities for the smallest values. This behaviour is very similar to what is involved, at the micrometric scale, in ductile fracture. The only difference is very likely due to the related length scales (nanometric instead of micrometric). Consequences of such a nano-ductile fracture mode observed at a temperature far below the glass transition temperature in glass is finally discussed.Comment: 12 pages, 8 figures, submitted to Journal of Physics: Condensed Matter; Invited talk at Glass and Optical Materials Division Fall 2002 Meeting, Pittsburgh, Pa, US

Multifractality at the spin quantum Hall transition

Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $\eta$ characterizing the decay of wave function correlations is equal to 1/4, at variance with the $r^{-1/2}$ decay of the diffusion propagator. The multifractality spectra of eigenfunctions and of two-point conductances are found to be close-to-parabolic, $\Delta_q\simeq q(1-q)/8$ and $X_q\simeq q(3-q)/4$.Comment: 4 pages, 3 figure

Spontaneous Symmetry Breaking in Directed Percolation with Many Colors: Differentiation of Species in the Gribov Process

A general field theoretic model of directed percolation with many colors that is equivalent to a population model (Gribov process) with many species near their extinction thresholds is presented. It is shown that the multicritical behavior is always described by the well known exponents of Reggeon field theory. In addition this universal model shows an instability that leads in general to a total asymmetry between each pair of species of a cooperative society.Comment: 4 pages, 2 Postscript figures, uses multicol.sty, submitte

Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states

One of the key features of non-equilibrium steady states (NESS) is the presence of nontrivial probability currents. We propose a general classification of NESS in which these currents play a central distinguishing role. As a corollary, we specify the transformations of the dynamic transition rates which leave a given NESS invariant. The formalism is most transparent within a continuous time master equation framework since it allows for a general graph-theoretical representation of the NESS. We discuss the consequences of these transformations for entropy production, present several simple examples, and explore some generalizations, to discrete time and continuous variables.Comment: 39 pages, 5 figures. Invited article for JSTAT Special Issue on 'Principles of Dynamics of Nonequilibrium Systems', held at the Newton Institute, Cambridge, UK, in 200