Long-time soliton dynamics via a coarse-grained space-time method
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arXiv
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| Format: | Preprint |
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2025
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| author | Pham, Dung N. Zager, Zoe Fan, Wentao Türeci, Hakan E. |
| author_facet | Pham, Dung N. Zager, Zoe Fan, Wentao Türeci, Hakan E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-time soliton dynamics via a coarse-grained space-time method Pham, Dung N. Zager, Zoe Fan, Wentao Türeci, Hakan E. Quantum Physics High Energy Physics - Phenomenology Optics 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. |
| title | Long-time soliton dynamics via a coarse-grained space-time method |
| topic | Quantum Physics High Energy Physics - Phenomenology Optics |
| url | https://arxiv.org/abs/2504.12286 |