Dynamics of Annealed Systems under External Fields: CTRW and the Fractional Fokker-Planck Equations

We consider the linear response of a system modelled by continuous-time random walks (CTRW) to an external field pulse of rectangular shape. We calculate the corresponding response function explicitely and show that it exhibits aging, i.e. that it is not translationally invariant in the time-domain. This result differs from that of systems which behave according to fractional Fokker-Planck equations

Small-World Rouse Networks as models of cross-linked polymers

We use the recently introduced small-world networks (SWN) to model cross-linked polymers, as an extension of the linear Rouse-chain. We study the SWN-dynamics under the influence of external forces. Our focus is on the structurally and thermally averaged SWN stretching, which we determine both numerically and analytically using a psudo-gap ansatz for the SWN-density of states. The SWN stretching is related to the probability of a random-walker to return to its origin on the SWN. We compare our results to the corresponding ones for Cayley trees.Comment: 14 pages, 4 figures. Preprint version, submitted to JC

The subdiffusive target problem: Survival probability

The asymptotic survival probability of a spherical target in the presence of a single subdiffusive trap or surrounded by a sea of subdiffusive traps in a continuous Euclidean medium is calculated. In one and two dimensions the survival probability of the target in the presence of a single trap decays to zero as a power law and as a power law with logarithmic correction, respectively. The target is thus reached with certainty, but it takes the trap an infinite time on average to do so. In three dimensions a single trap may never reach the target and so the survival probability is finite and, in fact, does not depend on whether the traps move diffusively or subdiffusively. When the target is surrounded by a sea of traps, on the other hand, its survival probability decays as a stretched exponential in all dimensions (with a logarithmic correction in the exponent for $d=2$). A trap will therefore reach the target with certainty, and will do so in a finite time. These results may be directly related to enzyme binding kinetics on DNA in the crowded cellular environment.Comment: 6 pages. References added, improved account of previous results and typos correcte

Dynamics of end-linked star polymer structures

In this work we focus on the dynamics of macromolecular networks formed by end-linking identical polymer stars. The resulting macromolecular network can then be viewed as consisting of spacers which connect branching points (the cores of the stars). We succeed in analyzing exactly, in the framework of the generalized Gaussian model, the eigenvalue spectrum of such networks. As applications we focus on several topologies, such as regular networks and dendrimers; furthermore, we compare the results to those found for regular hyperbranched structures. In so doing, we also consider situations in which the beads of the cores differ from the beads of the spacers. The analytical procedure which we use involves an exact real-space renormalization, which allows to relate the star-network to a (much simpler) network, in which each star is reduced to its core. It turns out that the eigenvalue spectrum of the star-polymer structure consists of two parts: One follows in terms of polynomial equations from the relaxation spectrum of the corresponding renormalized structure, while the second part involves the motion of the spacer chains themselves. Finally, we show exemplarily the situation for copolymeric dendrimers, calculate their spectra, and from them their storage and the loss moduli.Comment: 15 pages, 11 eps-figures include

Slow Excitation Trapping in Quantum Transport with Long-Range Interactions

Long-range interactions slow down the excitation trapping in quantum transport processes on a one-dimensional chain with traps at both ends. This is counter intuitive and in contrast to the corresponding classical processes with long-range interactions, which lead to faster excitation trapping. We give a pertubation theoretical explanation of this effect.Comment: 4 pages, 3 figure

Superdiffusion in Decoupled Continuous Time Random Walks

Continuous time random walk models with decoupled waiting time density are studied. When the spatial one jump probability density belongs to the Levy distribution type and the total time transition is exponential a generalized superdiffusive regime is established. This is verified by showing that the square width of the probability distribution (appropriately defined)grows as $t^{2/\gamma}$ with $0<\gamma\leq2$ when $t\to \infty$. An important connection of our results and those of Tsallis' nonextensive statistics is shown. The normalized q-expectation value of $x^2$ calculated with the corresponding probability distribution behaves exactly as $t^{2/\gamma}$ in the asymptotic limit.Comment: 9 pages (.tex file), 1 Postscript figures, uses revtex.st

Short-Term and Long-Term Collaboration Benefits on Individual Recall in Younger and Older Adults

A recent study of younger adults suggests that, compared to repeated individual recall trials, repeated collaborative recall trials produce better individual recall after a short delay (Blumen & Rajaram, 2008). Our study was designed to determine if such collaboration benefits would remain after a one-week delay, in both younger and older adults. Sixty younger (M age = 24.60) and 60 older (M age = 67.35) adults studied a list of words and then completed either two collaborative recall trials followed by two individual recall trials, or four individual recall trials. A five-min delay was inserted between the first three recall trials. The fourth recall trial was administered 1 week later. Collaborative recall was completed in groups of three individuals working together. Both younger and older adults benefitted from repeated collaborative recall trials to a greater extent than repeated individual recall trials, and such collaboration benefits remained after a one-week delay. This is the first demonstration of collaboration benefits on later individual recall at delays as long as 1 week, in both younger and older adults. Findings are discussed within the context of the negative effects of collaboration associated with group memory (collaborative inhibition) and the positive effects of collaboration associated with later individual memory (collaboration benefits)

Relaxation Properties of Small-World Networks

Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such structures by considering explicitly the probability for a random walker to be present at the origin. The results are intermediate between the corresponding ones for fractals and for Cayley trees.Comment: 16 pages, 6 figure

Quantum transport on small-world networks: A continuous-time quantum walk approach

We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWN). The SWN are build from a one-dimensional ring of N nodes by randomly introducing B additional bonds between them. The exciton dynamics is modeled by continuous-time quantum walks and we evaluate numerically the ensemble averaged transition probability to reach any node of the network from the initially excited one. For sufficiently large B we find that the quantum mechanical transport through the SWN is, first, very fast, given that the limiting value of the transition probability is reached very quickly; second, that the transport does not lead to equipartition, given that on average the exciton is most likely to be found at the initial node.Comment: 8 pages, 8 figures (high quality figures available upon request

Quantum transport on two-dimensional regular graphs

We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem can be treated in a large measure analytically. Some of these results carry over to graphs which obey open boundary conditions (OBCs), such as cylinders or rectangles. Under OBCs the long time transition probabilities (LPs) also display asymmetries for certain graphs, as a function of their particular sizes. Interestingly, these effects do not show up in the marginal distributions, obtained by summing the LPs along one direction.Comment: 22 pages, 11 figure, acceted for publication in J.Phys.