具有幂律相互作用的多体系统的自相似非平衡动力学
Self-similar non-equilibrium dynamics of a many-body system with power-law interactions
摘要：
幂律相互作用对远离平衡态的多体系统动力学的影响，远不如它们对静态和热力学性质的影响那么深入。为了深入了解这个问题，我们在这里介绍和分析一个不平衡的沉积过程中，一个给定的粒子的沉积速率取决于作为一个幂律的距离先前沉积的粒子。该模型从冷原子气体领域的最新实验进展中得出其相关性，这些冷原子气体是在被激发到高位里德堡态的原子通过幂律势相互作用的环境中研究的，幂律势转化为幂律激发率。这个系统的非平衡动力学结果是惊人的丰富。它具有自相似的演变，导致一个特征的幂律时间依赖性的可观测量，如粒子浓度，并导致在标度不变性的结构因子。我们的研究结果表明，在耗散里德堡气体的平衡之间的特征距离激发-通常被称为封锁半径-是不是一个静态的，而是一个动态的量。
英文摘要：
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power-law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations --- often referred to as the blockade radius --- is not a static but rather a dynamic quantity.
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