Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation study

Anisotropic disordered system are studied in this work within the random barrier model. In such systems the transition probabilities in different directions have different probability density functions. The frequency-dependent conductivity at low temperatures is obtained using an effective medium approximation. It is shown that the isotropic universal ac-conduction law, $\sigma \ln \sigma=u$, is recovered if properly scaled conductivity ($\sigma$) and frequency ($u$) variables are used.Comment: 5 pages, no figures, final form (with corrected equations

Computer simulation of Wheeler's delayed choice experiment with photons

We present a computer simulation model of Wheeler's delayed choice experiment that is a one-to-one copy of an experiment reported recently (V. Jacques {\sl et al.}, Science 315, 966 (2007)). The model is solely based on experimental facts, satisfies Einstein's criterion of local causality and does not rely on any concept of quantum theory. Nevertheless, the simulation model reproduces the averages as obtained from the quantum theoretical description of Wheeler's delayed choice experiment. Our results prove that it is possible to give a particle-only description of Wheeler's delayed choice experiment which reproduces the averages calculated from quantum theory and which does not defy common sense.Comment: Europhysics Letters (in press

The time resolution of the St. Petersburg paradox

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.Comment: 20 pages, 1 figur

Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model

We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional square lattice of lattice sizes up to L=4096. A detailed analysis of the probability distribution of the size, area, duration and radius of the avalanches will be given. To increase the accuracy of the determination of the avalanche exponents we introduce a new method for analyzing the data which reduces the finite-size effects of the measurements. The exponents of the avalanche distributions differ slightly from previous measurements and estimates obtained from a renormalization group approach.Comment: 6 pages, 6 figure

Anomalous diffusion and the first passage time problem

We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in terms of Fox or H-functions when the diffusion has zero drift. (2) For the nonzero drift case we obtain an analytical expression for the Laplace transform of the FPT distribution. (3) We express the FPT distribution in terms of a power series for the case of two absorbing barriers. The known results for ordinary diffusion (Brownian motion) are obtained as special cases of our more general results.Comment: 25 pages, 4 figure

Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices

A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind encountered in quantum physics the memory and CPU requirements of this method scale linearly with the dimension of the matrix. We derive a rigorous estimate of the statistical error, supporting earlier observations that the computational efficiency of this approach increases with matrix size. We use this method and an imaginary-time version of it to compute the energy and the specific heat of three different, exactly solvable, spin-1/2 models and compare with the exact results to study the dependence of the statistical errors on sample and matrix size.Comment: 24 pages, 24 figure

Fusion algebra of critical percolation

We present an explicit conjecture for the chiral fusion algebra of critical percolation considering Virasoro representations with no enlarged or extended symmetry algebra. The representations we take to generate fusion are countably infinite in number. The ensuing fusion rules are quasi-rational in the sense that the fusion of a finite number of these representations decomposes into a finite direct sum of these representations. The fusion rules are commutative, associative and exhibit an sl(2) structure. They involve representations which we call Kac representations of which some are reducible yet indecomposable representations of rank 1. In particular, the identity of the fusion algebra is a reducible yet indecomposable Kac representation of rank 1. We make detailed comparisons of our fusion rules with the recent results of Eberle-Flohr and Read-Saleur. Notably, in agreement with Eberle-Flohr, we find the appearance of indecomposable representations of rank 3. Our fusion rules are supported by extensive numerical studies of an integrable lattice model of critical percolation. Details of our lattice findings and numerical results will be presented elsewhere.Comment: 12 pages, v2: comments and references adde

W-Extended Fusion Algebra of Critical Percolation

Two-dimensional critical percolation is the member LM(2,3) of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p'). We consider the continuum scaling limit of this lattice model as a `rational' logarithmic conformal field theory with extended W=W_{2,3} symmetry and use a lattice approach on a strip to study the fundamental fusion rules in this extended picture. We find that the representation content of the ensuing closed fusion algebra contains 26 W-indecomposable representations with 8 rank-1 representations, 14 rank-2 representations and 4 rank-3 representations. We identify these representations with suitable limits of Yang-Baxter integrable boundary conditions on the lattice and obtain their associated W-extended characters. The latter decompose as finite non-negative sums of W-irreducible characters of which 13 are required. Implementation of fusion on the lattice allows us to read off the fusion rules governing the fusion algebra of the 26 representations and to construct an explicit Cayley table. The closure of these representations among themselves under fusion is remarkable confirmation of the proposed extended symmetry.Comment: 30 page

Corpuscular model of two-beam interference and double-slit experiments with single photons

We introduce an event-based corpuscular simulation model that reproduces the wave mechanical results of single-photon double slit and two-beam interference experiments and (of a one-to-one copy of an experimental realization) of a single-photon interference experiment with a Fresnel biprism. The simulation comprises models that capture the essential features of the apparatuses used in the experiment, including the single-photon detectors recording individual detector clicks. We demonstrate that incorporating in the detector model, simple and minimalistic processes mimicking the memory and threshold behavior of single-photon detectors is sufficient to produce multipath interference patterns. These multipath interference patterns are built up by individual particles taking one single path to the detector where they arrive one-by-one. The particles in our model are not corpuscular in the standard, classical physics sense in that they are information carriers that exchange information with the apparatuses of the experimental set-up. The interference pattern is the final, collective outcome of the information exchanges of many particles with these apparatuses. The interference patterns are produced without making reference to the solution of a wave equation and without introducing signalling or non-local interactions between the particles or between different detection points on the detector screen.Comment: Accepted for publication in J. Phys. Soc. Jpn