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A. Blumen

Publications and source records attributed to A. Blumen.

16 recordsLinked to original sources
arXiv2008

Dynamics of continuous-time quantum walks in restricted geometries

We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time. Indeed, a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms. By means of analytical and numerical investigations, we show that the finiteness and the inhomogeneity of the substrate jointly weaken the quantum walk performance. We further highlight the interplay between the quantum-walk dynamics and the underlying topology by studying the temporal evolution of the transfer probability distribution and the lower bound of long time averages.

quant-ph↗
arXiv2004

Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks

In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum for a general type of tree-like networks. Close to the percolation threshold we find characteristic scaling functions for the density of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for small lambda, where alpha_1 holds below and alpha_2 at the percolation threshold. In the range where the spectra are accessible from a numerical diagonalization procedure the two methods lead to very similar results.

cond-mat.stat-mech↗
arXiv2003

Scaling of star polymers: high order results

We extend existing renormalization group calculations for the exponents describing scaling of star polymers and polymer networks constituted by chains of different species (the so-called copolymer star exponents). Our four loop results find application in the description of various phenomena involving self-avoiding and random walks that interact.

cond-mat.soft↗
arXiv2003

Exactly solvable model of reactions on a random catalytic chain

In this paper we study a catalytically-activated A + A \to 0 reaction taking place on a one-dimensional regular lattice which is brought in contact with a reservoir of A particles. The A particles have a hard-core and undergo continuous exchanges with the reservoir, adsorbing onto the lattice or desorbing back to the reservoir. Some lattice sites possess special, catalytic properties, which induce an immediate reaction between two neighboring A particles as soon as at least one of them lands onto a catalytic site. We consider three situations for the spatial placement of the catalytic sites: regular, annealed random and quenched random. For all these cases we derive exact results for the partition function, and the disorder-averaged pressure per lattice site. We also present exact asymptotic results for the particles' mean density and the system's compressibility. The model studied here furnishes another example of a 1D Ising-type system with random multisite interactions which admits an exact solution.

cond-mat.stat-mech↗
arXiv2003

Exactly solvable model of A + A \to 0 reactions on a heterogeneous catalytic chain

We present an exact solution describing equilibrium properties of the catalytically-activated A + A \to 0 reaction taking place on a one-dimensional lattice, where some of the sites possess special "catalytic" properties. The A particles undergo continuous exchanges with the vapor phase; two neighboring adsorbed As react when at least one of them resides on a catalytic site (CS). We consider three situations for the CS distribution: regular, annealed random and quenched random. For all three CS distribution types, we derive exact results for the disorder-averaged pressure and present exact asymptotic expressions for the particles' mean density. The model studied here furnishes another example of a 1D Ising-type system with random multi-site interactions which admits an exact solution.

cond-mat.stat-mech↗
arXiv2002

Probing the local structure: macromolecular combs in external fields

Recent experimental methods allow to monitor the response of macromolecules to locally applied fields, complementing usual, mesoscopic techniques. Based on the Rouse-model and its extension to generalized Gaussian structures (GGS), we follow here the stretching of comb macromolecules under local fields. This leads to a wealth of informations about the structure: Namely, given the inhomogeneous architecture of combs, the dynamics and amount of stretching depend strongly on the position of the monomer on which the external fields act. We discuss both the theoretical and the experimental implications of our findings, given that micromanipulations can be supplemented by fluorescence measurements, which are very sensitive to changes in the intramolecular distances.

cond-mat↗
arXiv2001

Linear Response in Complex Systems: CTRW and the Fractional Fokker-Planck Equations

We consider the linear response of systems modelled by continuous-time random walks (CTRW) and by fractional Fokker-Planck equations under the influence of time-dependent external fields. We calculate the corresponding response functions explicitely. The CTRW curve exhibits aging, i.e. it is not translationally invariant in the time-domain. This is different from what happens under fractional Fokker-Planck conditions.

cond-mat.stat-mech↗
arXiv2001

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.

cond-mat.stat-mech↗
arXiv2000

Does strange kinetics imply unusual thermodynamics?

We introduce a fractional Fokker-Planck equation (FFPE) for Levy flights in the presence of an external field. The equation is derived within the framework of the subordination of random processes which leads to Levy flights. It is shown that the coexistence of anomalous transport and a potential displays a regular exponential relaxation towards the Boltzmann equilibrium distribution. The properties of the Levy-flight FFPE derived here are compared with earlier findings for subdiffusive FFPE. The latter is characterized by a non-exponential Mittag-Leffler relaxation to the Boltzmann distribution. In both cases, which describe strange kinetics, the Boltzmann equilibrium is reached and modifications of the Boltzmann thermodynamics are not required.

cond-mat.stat-mech↗
arXiv2000

Small-World Networks: Links with long-tailed distributions

Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing an AL depends on the chemical distance between the connected sites. We assume a power-law probability distribution and study random walkers on the network, focussing especially on their probability of being at the origin. We connect the results to Lévy Flights, which follow from a mean field variant of our model.

cond-mat.stat-mech↗
arXiv2000

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.

cond-mat.stat-mech↗
arXiv2000

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.

cond-mat.stat-mech↗
arXiv1999

Anchoring of polymers by traps randomly placed on a line

We study dynamics of a Rouse polymer chain, which diffuses in a three-dimensional space under the constraint that one of its ends, referred to as the slip-link, may move only along a one-dimensional line containing randomly placed, immobile, perfect traps. For such a model we compute exactly the time evolution of the probability $P_{sl}(t)$ that the chain slip-link will not encounter any of the traps until time $t$ and consequently, that until this time the chain will remain mobile.

cond-mat.stat-mech↗
arXiv1997

Kinetic description of diffusion-limited reactions in random catalytic media

We study the kinetics of bimolecular, catalytically-activated reactions (CARs) in d-dimensions. The elementary reaction act between reactants takes place only when these meet in the vicinity of a catalytic site; such sites are assumed to be immobile and randomly distributed in space. For CARs we develop a kinetic formalism, based on Collins-Kimball-type ideas; within this formalism we obtain explicit expressions for the effective reaction rates and for the decay of the reactants' concentrations.

cond-mat↗
arXiv1996

Direct Energy Transfer in Systems of Polymerized Acceptors

We study the direct incoherent energy transfer from an immobile excited donor molecule to acceptor molecules, which are all attached to polymer chains, randomly arranged in a viscous solvent. The decay forms are found explicitly, in terms of an optimal-fluctuation method, for arbitrary conformations of polymers.

cond-mat↗