Structure of the stationary state of the asymmetric target process
| dc.creator | Luck, J. M. | |
| dc.creator | Godreche, C. | |
| dc.date | 2007-05-07 | |
| dc.date.accessioned | 2026-07-07T08:22:01Z | |
| dc.date.available | 2026-07-07T08:22:01Z | |
| dc.description | We introduce a novel migration process, the target process. This process is dual to the zero-range process (ZRP) in the sense that, while for the ZRP the rate of transfer of a particle only depends on the occupation of the departure site, it only depends on the occupation of the arrival site for the target process. More precisely, duality associates to a given ZRP a unique target process, and vice-versa. If the dynamics is symmetric, i.e., in the absence of a bias, both processes have the same stationary-state product measure. In this work we focus our interest on the situation where the latter measure exhibits a continuous condensation transition at some finite critical density $ρ_c$, irrespective of the dimensionality. The novelty comes from the case of asymmetric dynamics, where the target process has a nontrivial fluctuating stationary state, whose characteristics depend on the dimensionality. In one dimension, the system remains homogeneous at any finite density. An alternating scenario however prevails in the high-density regime: typical configurations consist of long alternating sequences of highly occupied and less occupied sites. The local density of the latter is equal to $ρ_c$ and their occupation distribution is critical. In dimension two and above, the asymmetric target process exhibits a phase transition at a threshold density $ρ_0$ much larger than $ρ_c$. The system is homogeneous at any density below $ρ_0$, whereas for higher densities it exhibits an extended condensate elongated along the direction of the mean current, on top of a critical background with density $ρ_c$. | |
| dc.description | 30 pages, 16 figures | |
| dc.identifier | https://arxiv.org/abs/0705.0907 | |
| dc.identifier | http://arxiv.org/abs/0705.0907 | |
| dc.identifier | J. Stat. Mech. (2007) P08005 | |
| dc.identifier | doi:10.1088/1742-5468/2007/08/P08005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135511 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Structure of the stationary state of the asymmetric target process | |
| dc.type | text |