No directed fractal percolation in zero area

We show that fractal (or "Mandelbrot") percolation in two dimensions produces a set containing no directed paths, when the set produced has zero area. This improves a similar result by the first author in the case of constant retention probabilities to the case of retention probabilities approaching 1

Constraints on neutrino decay lifetime using long-baseline charged and neutral current data

We investigate the status of a scenario involving oscillations and decay for charged and neutral current data from the MINOS and T2K experiments. We first present an analysis of charged current neutrino and anti-neutrino data from MINOS in the framework of oscillation with decay and obtain a best fit for non-zero decay parameter $\alpha_3$. The MINOS charged and neutral current data analysis results in the best fit for $|\Delta m_{32}^2| = 2.34\times 10^{-3}$~eV$^2$, $\sin^2 \theta_{23} = 0.60$ and zero decay parameter, which corresponds to the limit for standard oscillations. Our combined MINOS and T2K analysis reports a constraint at the 90\% confidence level for the neutrino decay lifetime $\tau_3/m_3 > 2.8 \times 10^{-12}$~s/eV. This is the best limit based only on accelerator produced neutrinos

Relativistic Doppler effect in quantum communication

When an electromagnetic signal propagates in vacuo, a polarization detector cannot be rigorously perpendicular to the wave vector because of diffraction effects. The vacuum behaves as a noisy channel, even if the detectors are perfect. The ``noise'' can however be reduced and nearly cancelled by a relative motion of the observer toward the source. The standard definition of a reduced density matrix fails for photon polarization, because the transversality condition behaves like a superselection rule. We can however define an effective reduced density matrix which corresponds to a restricted class of positive operator-valued measures. There are no pure photon qubits, and no exactly orthogonal qubit states.Comment: 10 pages LaTe

Charge and Spin Transport in the One-dimensional Hubbard Model

In this paper we study the charge and spin currents transported by the elementary excitations of the one-dimensional Hubbard model. The corresponding current spectra are obtained by both analytic methods and numerical solution of the Bethe-ansatz equations. For the case of half-filling, we find that the spin-triplet excitations carry spin but no charge, while charge $\eta$-spin triplet excitations carry charge but no spin, and both spin-singlet and charge $\eta$-spin-singlet excitations carry neither spin nor charge currents.Comment: 24 pages, 14 figure

Neutrino Decay and Solar Neutrino Seasonal Effect

We consider the possibility of solar neutrino decay as a sub-leading effect on their propagation between production and detection. Using current oscillation data, we set a new lower bound to the $\nu_2$ neutrino lifetime at $\tau_2\, /\, m_2 \geq 7.2 \times 10^{-4}\,\,\hbox{s}\,.\,\hbox{eV}^{-1}$ at $99\%\,$C.L.. Also, we show how seasonal variations in the solar neutrino data can give interesting additional information about neutrino lifetime

Quantum and classical descriptions of a measuring apparatus

A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation, and then it must be given a classical description so that the result of the measurement appears as objective reality. Alternatively, the apparatus may always be treated by quantum mechanics, and be measured by a second apparatus which has such a dual description. This article examines whether these two different descriptions are mutually consistent. It is shown that if the dynamical variable used in the first apparatus is represented by an operator of the Weyl-Wigner type (for example, if it is a linear coordinate), then the conversion from quantum to classical terminology does not affect the final result. However, if the first apparatus encodes the measurement in a different type of operator (e.g., the phase operator), the two methods of calculation may give different results.Comment: 18 pages LaTeX (including one encapsulated PostScript figure

Statistics of opinion domains of the majority-vote model on a square lattice

The existence of juxtaposed regions of distinct cultures in spite of the fact that people's beliefs have a tendency to become more similar to each other's as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size $L$ and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with $L^2$ whereas the size of the largest cluster grows with $\ln L^2$. The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model -- Axelrod's model -- we found that these opinion domains are unstable to the effect of a thermal-like noise