Structure of the stationary state of the asymmetric target process
| Autor: | Luck, J. M., Godreche, C. |
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| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | J. Stat. Mech. (2007) P08005 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-5468/2007/08/P08005 |
| Popis: | 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 $\rho_c$, 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 $\rho_c$ and their occupation distribution is critical. In dimension two and above, the asymmetric target process exhibits a phase transition at a threshold density $\rho_0$ much larger than $\rho_c$. The system is homogeneous at any density below $\rho_0$, 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 $\rho_c$. Comment: 30 pages, 16 figures |
| Databáze: | arXiv |
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