AUTHOR=Muñoz-Gil Gorka , Garcia-March Miguel Angel , Manzo Carlo , Celi Alessio , Lewenstein Maciej TITLE=Diffusion Through a Network of Compartments Separated by Partially-Transmitting Boundaries JOURNAL=Frontiers in Physics VOLUME=7 YEAR=2019 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00031 DOI=10.3389/fphy.2019.00031 ISSN=2296-424X ABSTRACT=

We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length L and the boundaries transmittance T. We identify two relevant spatio-temporal scales that provide alternative descriptions of the dynamics: (i) the microscale, in which the particle position is monitored at constant time intervals; and (ii) the mesoscale, in which it is monitored only when the particle crosses a boundary between compartments. Both descriptions provide—by construction—the same long time behavior. The analytical description obtained at the proposed mesoscale allows for a complete characterization of the complex movement at the microscale, thus representing a fruitful approach for this kind of systems. We show that the presence of disorder in the transmittance is a necessary condition to induce anomalous diffusion, whereas the spatial heterogeneity reduces the degree of subdiffusion and, in some cases, can even compensate for the disorder induced by the stochastic transmittance.