摘要翻译：
我们引入了一个新的迁移过程，目标过程。这一过程与零程过程(ZRP)是对偶的，因为对于ZRP来说，粒子的转移速率只取决于对离开位置的占用，而对于目标过程来说，它只取决于对到达位置的占用。更确切地说，对偶性与给定的ZRP相关联的是一个唯一的目标过程，反之亦然。如果动力学是对称的，即在没有偏置的情况下，两个过程具有相同的定态积测度。在本工作中，我们的兴趣集中在后者测度在有限的临界密度$\Rho_c$下表现出连续凝聚跃迁的情形，而与维数无关。其新颖之处来自于非对称动力学的情形，即目标过程具有非平凡的波动定态，其特征依赖于维数。在一维中，系统在任何有限密度下都保持均匀。然而，在高密度区域中，一种交替的情况普遍存在：典型的配置由高度占用和较少占用的长的交替序列组成。后者的局域密度等于$\Rho_c$，它们的占位分布是至关重要的。在二维及二维以上，非对称靶过程在阈值密度$\Rho_0$远大于$\Rho_C$处呈现相变。在任何密度低于$\RhO_0$时，该体系都是均匀的，而对于较高密度，在密度为$\RhO_C$的临界背景之上，它表现出沿平均电流方向延伸的凝析油。
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英文标题：
《Structure of the stationary state of the asymmetric target process》
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作者：
J.M. Luck and C. Godreche
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  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 $\rho_c$.
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PDF链接：
https://arxiv.org/pdf/705.0907