Trapping in complex networks

We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density $\rho(t)$ of random walkers in the presence of one or multiple traps with concentration $c$. We show using theory and simulations that in ER networks, while for short times $\rho(t) \propto \exp(-Act)$, for longer times $\rho(t)$ exhibits a more complex behavior, with explicit dependence on both the number of traps and the size of the network. In SF networks we reveal the significant impact of the trap's location: $\rho(t)$ is drastically different when a trap is placed on a random node compared to the case of the trap being on the node with the maximum connectivity. For the latter case we find \rho(t)\propto\exp\left[-At/N^\frac{\gamma-2}{\gamma-1}\av{k}\right] for all $\gamma>2$, where $\gamma$ is the exponent of the degree distribution $P(k)\propto k^{-\gamma}$.Comment: Appendix adde

Transition time asymptotics of queue-based activation protocols in random-access networks

We consider networks where each node represents a server with a queue. An active node deactivates at unit rate. An inactive node activates at a rate that depends on its queue length, provided none of its neighbors is active. For complete bipartite networks, in the limit as the queues become large, we compute the average transition time between the two states where one half of the network is active and the other half is inactive. We show that the law of the transition time divided by its mean exhibits a trichotomy, depending on the activation rate functions

Kinetics of diffusion-limited catalytically-activated reactions: An extension of the Wilemski-Fixman approach

We study kinetics of diffusion-limited catalytically-activated $A + B \to B$ reactions taking place in three dimensional systems, in which an annihilation of diffusive $A$ particles by diffusive traps $B$ may happen only if the encounter of an $A$ with any of the $B$s happens within a special catalytic subvolumen, these subvolumens being immobile and uniformly distributed within the reaction bath. Suitably extending the classical approach of Wilemski and Fixman (G. Wilemski and M. Fixman, J. Chem. Phys. \textbf{58}:4009, 1973) to such three-molecular diffusion-limited reactions, we calculate analytically an effective reaction constant and show that it comprises several terms associated with the residence and joint residence times of Brownian paths in finite domains. The effective reaction constant exhibits a non-trivial dependence on the reaction radii, the mean density of catalytic subvolumens and particles' diffusion coefficients. Finally, we discuss the fluctuation-induced kinetic behavior in such systems.Comment: To appear in J. Chem. Phy

Heat flow in chains driven by thermal noise

We consider the large deviation function for a classical harmonic chain composed of N particles driven at the end points by heat reservoirs, first derived in the quantum regime by Saito and Dhar and in the classical regime by Saito and Dhar and Kundu et al. Within a Langevin description we perform this calculation on the basis of a standard path integral calculation in Fourier space. The cumulant generating function yielding the large deviation function is given in terms of a transmission Green's function and is consistent with the fluctuation theorem. We find a simple expression for the tails of the heat distribution which turn out to decay exponentially. We, moreover, consider an extension of a single particle model suggested by Derrida and Brunet and discuss the two-particle case. We also discuss the limit for large N and present a closed expression for the cumulant generating function. Finally, we present a derivation of the fluctuation theorem on the basis of a Fokker-Planck description. This result is not restricted to the harmonic case but is valid for a general interaction potential between the particles.Comment: Latex: 26 pages and 9 figures, appeared in J. Stat. Mech. P04005 (2012

Quantum state estimation and large deviations

In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends previous results concerning the estimation of the spectrum of \rho. We show that it is consistent (i.e. the original input state \rho is recovered with certainty if N \to \infty), analyze its large deviation behavior, and calculate explicitly the corresponding rate function which describes the exponential decrease of error probabilities in the limit N \to \infty. Finally we discuss the question whether the proposed scheme provides the fastest possible decay of error probabilities.Comment: LaTex2e, 40 pages, 2 figures. Substantial changes in Section 4: one new subsection (4.1) and another (4.2 was 4.1 in the previous version) completely rewritten. Minor changes in Sect. 2 and 3. Typos corrected. References added. Accepted for publication in Rev. Math. Phy

Tunneling and Metastability of continuous time Markov chains

We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the capacity and of the stationary measure of the metastable states

Discrete Particle Swarm Optimization for the minimum labelling Steiner tree problem

Particle Swarm Optimization is an evolutionary method inspired by the social behaviour of individuals inside swarms in nature. Solutions of the problem are modelled as members of the swarm which fly in the solution space. The evolution is obtained from the continuous movement of the particles that constitute the swarm submitted to the effect of the inertia and the attraction of the members who lead the swarm. This work focuses on a recent Discrete Particle Swarm Optimization for combinatorial optimization, called Jumping Particle Swarm Optimization. Its effectiveness is illustrated on the minimum labelling Steiner tree problem: given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes, whose edges have the smallest number of distinct labels

Entropy production and fluctuation relations for a KPZ interface

We study entropy production and fluctuation relations in the restricted solid-on-solid growth model, which is a microscopic realization of the KPZ equation. Solving the one dimensional model exactly on a particular line of the phase diagram we demonstrate that entropy production quantifies the distance from equilibrium. Moreover, as an example of a physically relevant current different from the entropy, we study the symmetry of the large deviation function associated with the interface height. In a special case of a system of length L=4 we find that the probability distribution of the variation of height has a symmetric large deviation function, displaying a symmetry different from the Gallavotti-Cohen symmetry.Comment: 21 pages, 5 figure