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

• URL: http://arxiv.org/abs/2504.12286v2
• Date: Sun, 20 Apr 2025 19:53:25 GMT
• Title: Long-time soliton dynamics via a coarse-grained space-time method
• Abstract summary: We extend a coarse-graining method to spacetime using a dual-mesh construction based on the Minkowski-metric.<n>We uncover long-lived bound states - "Schwinger atoms" - in which a soliton is trapped by a fixed central charge.<n>Our results also suggest the possibility of quantum simulation of relativistic quantum field theories.
• Score: 7.743463245493229
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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