论文标题
一个具有移动性边缘的一维不合增长模型的家庭不平衡
Imbalance for a family of one-dimensional incommensurate models with mobility edges
论文作者
论文摘要
在本文中，我们研究了具有移动性边缘的一维Aubry-Andre-Harper（AAH）模型的四个概括。我们在人口不平衡方面绘制了一个相图，并查看稳态不平衡的系统大小依赖性。我们发现不平衡与系统参数的非单调行为相矛盾，即初始不平衡的放松仅由扩展状态数与局部状态数的比率固定。我们建议存在无量纲参数，这取决于单个粒子局部状态，单个粒子扩展状态和这些状态的平均参与比的比例。这些成分完全控制了长期限制的失衡，我们提供了这一主张的数值证据。在考虑的四个模型中，其中三个具有有趣的二元关系，并且它们的位置移动边缘是已知的。其中一个模型（下一个最近的邻居耦合）没有已知的双重性，但是迁移率边缘存在，并且该模型已实现。我们的发现是理解具有不一致电位的有趣模型家族中非平衡现象的重要一步。
In this paper, we look at four generalizations of the one dimensional Aubry-Andre-Harper (AAH) model which possess mobility edges. We map out a phase diagram in terms of population imbalance, and look at the system size dependence of the steady state imbalance. We find non-monotonic behaviour of imbalance with system parameters, which contradicts the idea that the relaxation of an initial imbalance is fixed only by the ratio of number of extended states to number of localized states. We propose that there exists dimensionless parameters, which depend on the fraction of single particle localized states, single particle extended states and the mean participation ratio of these states. These ingredients fully control the imbalance in the long time limit and we present numerical evidence of this claim. Among the four models considered, three of them have interesting duality relations and their location of mobility edges are known. One of the models (next nearest neighbour coupling) has no known duality but mobility edge exists and the model has been experimentally realized. Our findings are an important step forward to understanding non-equilibrium phenomena in a family of interesting models with incommensurate potentials.
