Superdiffusion in a class of networks with marginal long-range connections

A class of cubic networks composed of a regular one-dimensional lattice and a set of long-range links is introduced. Networks parametrized by a positive integer k are constructed by starting from a one-dimensional lattice and iteratively connecting each site of degree 2 with a $k$th neighboring site of degree 2. Specifying the way pairs of sites to be connected are selected, various random and regular networks are defined, all of which have a power-law edge-length distribution of the form $P_>(l)\sim l^{-s}$ with the marginal exponent s=1. In all these networks, lengths of shortest paths grow as a power of the distance and random walk is super-diffusive. Applying a renormalization group method, the corresponding shortest-path dimensions and random-walk dimensions are calculated exactly for k=1 networks and for k=2 regular networks; in other cases, they are estimated by numerical methods. Although, s=1 holds for all representatives of this class, the above quantities are found to depend on the details of the structure of networks controlled by k and other parameters.Comment: 10 pages, 9 figure

Nonuniversal and anomalous critical behavior of the contact process near an extended defect

We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of $\lambda(l)-\lambda(\infty) = A l^{-s}$, $l$ being the distance from the surface. We concentrate on the marginal situation, $s=1/\nu_{\perp}$, where $\nu_{\perp}$ is the critical exponent of the spatial correlation length, and study the local critical properties of the one-dimensional model by Monte Carlo simulations. The system exhibits a rich surface critical behavior. For weaker local activation rates, $A<A_c$, the phase transition is continuous, having an order-parameter critical exponent, which varies continuously with $A$. For stronger local activation rates, $A>A_c$, the phase transition is of mixed order: the surface order parameter is discontinuous, at the same time the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. The mixed-order transition regime is analogous to that observed recently at a multiple junction and can be explained by the same type of scaling theory.Comment: 8 pages, 8 figure

Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field

We study nonequilibrium dynamics of the quantum Ising chain at zero temperature when the transverse field is varied stochastically. In the equivalent fermion representation, the equation of motion of Majorana operators is derived in the form of a one-dimensional, continuous-time quantum random walk with stochastic, time-dependent transition amplitudes. This type of external noise gives rise to decoherence in the associated quantum walk and the semiclassical wave-packet generally has a diffusive behavior. As a consequence, in the quantum Ising chain, the average entanglement entropy grows in time as $t^{1/2}$ and the logarithmic average magnetization decays in the same form. In the case of a dichotomous noise, when the transverse-field is changed in discrete time-steps, $\tau$, there can be excitation modes, for which coherence is maintained, provided their energy satisfies $\epsilon_k \tau\approx n\pi$ with a positive integer $n$. If the dispersion of $\epsilon_k$ is quadratic, the long-time behavior of the entanglement entropy and the logarithmic magnetization is dominated by these ballistically traveling coherent modes and both will have a $t^{3/4}$ time-dependence.Comment: 12 pages, 10 figure

Metal-rich or misclassified? The case of four RR Lyrae stars

We analysed the light curve of four, apparently extremely metal-rich fundamental-mode RR Lyrae stars. We identified two stars, MT Tel and ASAS J091803-3022.6 as RRc (first-overtone) pulsators that were misclassified as RRab ones in the ASAS survey. In the case of the other two stars, V397 Gem and ASAS J075127-4136.3, we could not decide conclusively, as they are outliers in the period-Fourier-coefficient space from the loci of both classes, but their photometric metallicities also favour the RRc classification.Comment: 5 pages, 2 figures, published in IBVS: http://ibvs.konkoly.hu/cgi-bin/IBVS?617

The effect of asymmetric disorder on the diffusion in arbitrary networks

Considering diffusion in the presence of asymmetric disorder, an exact relationship between the strength of weak disorder and the electric resistance of the corresponding resistor network is revealed, which is valid in arbitrary networks. This implies that the dynamics are stable against weak asymmetric disorder if the resistance exponent $\zeta$ of the network is negative. In the case of $\zeta>0$, numerical analyses of the mean first-passage time $\tau$ on various fractal lattices show that the logarithmic scaling of $\tau$ with the distance $l$, $\ln\tau\sim l^{\psi}$, is a general rule, characterized by a new dynamical exponent $\psi$ of the underlying lattice.Comment: 5 pages, 4 figure

Percolation theory suggests some general features in range margins across environmental gradients

The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range margins is fragmentation, caused internally by population dynamics or externally by the limited availability of suitable habitat sites. We study both causes, and describe the transition from a connected to a fragmented state across space by means of a gradient metapopulation model. The main features of our approach are the following. 1) Inhomogeneities can occur at two spatial scales: there is a broad-scale gradient, which can be patterned by fine-scale heterogeneities. The latter is implemented by dispersing a variable number of small obstacles over the terrain, which can be penetrable or unpenetrable by the spreading species. 2) We study the occupancy of this terrain in a steady-state on two temporal scales: in snapshots and by long-term averages. The simulations reveal some general scaling laws that are applicable in various environments, independently of the mechanism of fragmentation. The edge of the connected region (the hull) is a fractal with dimension 7/4. Its width and length changes with the gradient according to universal scaling laws, that are characteristic for percolation transitions. The results suggest that percolation theory is a powerful tool for understanding the structure of range margins in a broad variety of real-life scenarios, including those in which the environmental gradient is combined with fine-scale heterogeneity. This provides a new method for comparing the range margins of different species in various geographic regions, and monitoring range shifts under climate change.Comment: 17 pages, 5 figure

Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields

In transverse-field Ising models, disorder in the couplings gives rise to a drastic reduction of the critical energy gap and, accordingly, to an unfavorable, slower-than-algebraic scaling of the density of defects produced when the system is driven through its quantum critical point. By applying Kibble-Zurek theory and numerical calculations, we demonstrate in the one-dimensional model that the scaling of defect density with annealing time can be made algebraic by balancing the coupling disorder with suitably chosen inhomogeneous driving fields. Depending on the tail of the coupling distribution at zero, balancing can be either perfect, leading to the well-known inverse-square law of the homogeneous system, or partial, still resulting in an algebraic decrease but with a smaller, non-universal exponent. We also study defect production during an environment-temperature quench of the open variant of the model in which the system is slowly cooled down to its quantum critical point. According to our scaling and numerical results, balanced disorder leads again to an algebraic temporal decrease of the defect density.Comment: 11 pages, 6 figure

Anomalous diffusion in disordered multi-channel systems

We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong disorder renormalization group method and Monte Carlo simulations are used. Generally, we observe anomalous diffusion, where the average distance travelled by the particle, []_{av}, has a power-law time-dependence []_{av} ~ t^{\mu_K(v)}, with a diffusion exponent 0 \le \mu_K(v) \le 1. In the presence of left-right symmetry of the distribution of random rates, the recurrent point of the multi-channel system is independent of K, and the diffusion exponent is found to increase with K and decrease with v. In the absence of this symmetry, the recurrent point may be shifted with K and the current can be reversed by varying the lane change rate v.Comment: 16 pages, 7 figure