Bosonic reaction-diffusion processes on scale-free networks - Condensed Matter > Statistical MechanicsReport as inadecuate

Bosonic reaction-diffusion processes on scale-free networks - Condensed Matter > Statistical Mechanics - Download this document for free, or read online. Document in PDF available to download.

Abstract: Reaction-diffusion processes can be adopted to model a large number ofdynamics on complex networks, such as transport processes or epidemicoutbreaks. In most cases, however, they have been studied from a fermionicperspective, in which each vertex can be occupied by at most one particle.While still useful, this approach suffers from some drawbacks, the mostimportant probably being the difficulty to implement reactions involving morethan two particles simultaneously. Here we introduce a general framework forthe study of bosonic reaction-diffusion processes on complex networks, in whichthere is no restriction on the number of interacting particles that a vertexcan host. We describe these processes theoretically by means of continuous timeheterogeneous mean-field theory and divide them into two main classes: steadystate and monotonously decaying processes. We analyze specific examples of bothbehaviors within the class of one-species process, comparing the resultswhenever possible with the corresponding fermionic counterparts. We find thatthe time evolution and critical properties of the particle density areindependent of the fermionic or bosonic nature of the process, whiledifferences exist in the functional form of the density of occupied vertices ina given degree class k. We implement a continuous time Monte Carlo algorithm,well suited for general bosonic simulations, which allow us to confirm theanalytical predictions formulated within mean-field theory. Our results, bothat the theoretical and numerical level, can be easily generalized to tacklemore complex, multi-species, reaction-diffusion processes, and open a promisingpath for a general study and classification of this kind of dynamical systemson complex networks.

Author: Andrea Baronchelli, Michele Catanzaro, Romualdo Pastor-Satorras


Related documents