Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914926260387840 |
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| author | Vercesi, Francesco Poirier, Susie Minguzzi, Anna Canet, Léonie |
| author_facet | Vercesi, Francesco Poirier, Susie Minguzzi, Anna Canet, Léonie |
| contents | We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this regime, the behaviour of the large wavelength modes is captured by the Kardar-Parisi-Zhang equation, determining universal scaling and statistical properties. We present numerical evidence of the existence of an additional scale-invariant regime, with dynamical scaling exponent $z=1$, emerging at scales which are intermediate between the microscopic, intrinsic to the modulational instability, and the macroscopic ones. We argue that this new regime is a signature of the universality class corresponding to the inviscid limit of the Kardar-Parisi-Zhang equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08530 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation Vercesi, Francesco Poirier, Susie Minguzzi, Anna Canet, Léonie Statistical Mechanics Quantum Gases Chaotic Dynamics We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this regime, the behaviour of the large wavelength modes is captured by the Kardar-Parisi-Zhang equation, determining universal scaling and statistical properties. We present numerical evidence of the existence of an additional scale-invariant regime, with dynamical scaling exponent $z=1$, emerging at scales which are intermediate between the microscopic, intrinsic to the modulational instability, and the macroscopic ones. We argue that this new regime is a signature of the universality class corresponding to the inviscid limit of the Kardar-Parisi-Zhang equation. |
| title | Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation |
| topic | Statistical Mechanics Quantum Gases Chaotic Dynamics |
| url | https://arxiv.org/abs/2404.08530 |