We study diffusion on a periodic billiard table with an infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a Levy walk combining exponentially distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients, which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards.
Giampaolo Cristadoro, Thomas Gilbert, Marco Lenci, David P. Sanders (2014). Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards. PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS, 90(5), 050102-1-050102-5 [10.1103/PhysRevE.90.050102].
Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards
CRISTADORO, GIAMPAOLO;LENCI, MARCO;
2014
Abstract
We study diffusion on a periodic billiard table with an infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a Levy walk combining exponentially distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients, which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.