受驱排斥格子气中的电流量子化和分形结构
Current quantization and fractal hierarchy in a driven repulsive lattice gas
摘要：
被驱动的晶格气体被广泛认为是集体失平衡现象的典范。虽然这些模型通常是用最近邻相互作用来研究的，但许多经验驱动系统都是由缓慢衰减的相互作用（如偶极-偶极和范德华力）所主导的。受这个能隙的启发，我们研究了零温下具有缓慢衰减排斥作用的受驱动格子气的非平衡定态。通过对粒子电流作为密度和驱动场的函数的数值和分析计算，我们确定了（i）绝缘和导电状态之间的突然击穿过渡，（ii）电流量子化成离散相，其中有限电流流动具有无穷大的微分电阻率，以及（iii）与数论的Farey序列相关的分形层次的激发。我们认为，这些影响的起源是尺度之间的竞争，这也导致了违反直觉的现象，结晶态可以通过增加密度熔化。
英文摘要：
Driven lattice gases are widely regarded as the paradigm of collective phenomena out of equilibrium. While such models are usually studied with nearest-neighbor interactions, many empirical driven systems are dominated by slowly decaying interactions such as dipole-dipole and Van der Waals forces. Motivated by this gap, we study the non-equilibrium stationary state of a driven lattice gas with slow-decayed repulsive interactions at zero temperature. By numerical and analytical calculations of the particle current as a function of the density and of the driving field, we identify (i) an abrupt breakdown transition between insulating and conducting states, (ii) current quantization into discrete phases where a finite current flows with infinite differential resistivity, and (iii) a fractal hierarchy of excitations, related to the Farey sequences of number theory. We argue that the origin of these effects is the competition between scales, which also causes the counterintuitive phenomenon that crystalline states can melt by increasing the density.
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