标题： 通过粗粒度时空方法的长时间孤立子动力学 显示英文标题

标题： Long-time soliton dynamics via a coarse-grained space-time method

摘要： 我们研究在一类扰动下的Sine-Gordon(SG)模型的长时间动力学，其量子场论对应——通过玻色化——对应于描述狄拉克费米子1+1D相对论QED的带质量施温格模型。经典SG解为该量子理论中的非微扰效应提供了关键见解，但捕捉它们的长时间行为带来了重大的数值挑战。为了解决这个问题，我们扩展了一种粗粒化方法，使用基于闵可夫斯基度规的双网格构造来处理时空。我们首先将该方法与已广泛研究的描述约瑟夫森传输线(JTLs)中磁通量子动力学的SG模型变体进行验证，其中存在解析和数值基准。然后我们将该方法应用于受施温格启发的SG模型，并发现长寿命的束缚态——“施温格原子”——其中孤子被固定的中心电荷所捕获。在某些区域，系统表现出极限环，产生类似正电子偶素的相反电荷孤子态，而在其他区域这种形成则被抑制。获取此类长时间解需要在有限计算域上严格实现向外边界条件，这些条件提供辐射耗散，以允许向仅存在于无限域中的状态弛豫。在这里我们提供了这样的构造。我们的结果还表明，使用JTLs进行相对论量子场论的类比量子模拟的可能性。这些结果展示了时空粗粒化方法在探测非线性场论中非微扰结构形成方面的效用。 显示英文摘要

摘要： We investigate the long-time dynamics of the Sine-Gordon (SG) model under a class of perturbations whose quantum field theoretic analog - via bosonization - corresponds to the massive Schwinger model describing 1+1D relativistic QED of Dirac fermions. Classical SG solutions offer critical insight into non-perturbative effects in this quantum theory, but capturing their long-time behavior poses significant numerical challenges. To address this, we extend a coarse-graining method to spacetime using a dual-mesh construction based on the Minkowski-metric. We first validate the approach against the well-studied variant of the SG model describing magnetic fluxon dynamics in Josephson transmission lines (JTLs), where analytical and numerical benchmarks exist. We then apply the method to the Schwinger-inspired SG model and uncover long-lived bound states - "Schwinger atoms" - in which a soliton is trapped by a fixed central charge. In certain regimes, the system exhibits limit cycles that give rise to positronium-like states of oppositely charged solitons, while in others such formation is suppressed. Accessing such long-time solutions requires a rigorous implementation of outgoing boundary conditions on a finite computational domain that provide radiative dissipation to allow relaxation toward states that exist only in an infinite domain. Here we provide such a construction. Our results also suggest the possibility of analog quantum simulation of relativistic quantum field theories with JTLs. These results demonstrate the utility of spatio-temporal coarse-graining methodology for probing non-perturbative structure formation in non-linear field theories.