Out-of-time-ordered correlators for turbulent fields: a quantum-classical correspondence
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911467447517184 |
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| author | Nakata, Motoki |
| author_facet | Nakata, Motoki |
| contents | An extended formulation of out-of-time-ordered correlators (OTOCs), which quantify noncommutative operator growth and information scrambling in quantum many-body systems, is developed for turbulence dynamics as a representative of non-canonical Hamiltonian systems. Based on the Wigner-Weyl transform and the Moyal bracket formalism, the semiclassical limit of OTOC for turbulent plasmas governed by the Hasegawa-Mima equation is derived as an ensemble-averaged squared Lie-Poisson bracket between two chosen functionals of the turbulent fields. The classical-limit OTOC provides a quantitative measure of how a variational perturbation applied to one functional propagates across scales in the turbulent dynamics and how it affects another functional at a later time, thereby capturing scale-dependent or field-dependent transfer processes. In a quasilinear approximation with a strong zonal flow, we derive an inverse-square decay of the OTOC with the time lag, indicating an algebraic suppression of the zonal-mode response to perturbations of the non-zonal fields. This behavior is attributed to zonal-flow shearing, which rapidly scrambles the non-zonal perturbation toward higher wavenumbers, and consequently reduces the low-wavenumber non-zonal content that can feed back onto large-scale zonal modes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21710 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Out-of-time-ordered correlators for turbulent fields: a quantum-classical correspondence Nakata, Motoki Plasma Physics Fluid Dynamics An extended formulation of out-of-time-ordered correlators (OTOCs), which quantify noncommutative operator growth and information scrambling in quantum many-body systems, is developed for turbulence dynamics as a representative of non-canonical Hamiltonian systems. Based on the Wigner-Weyl transform and the Moyal bracket formalism, the semiclassical limit of OTOC for turbulent plasmas governed by the Hasegawa-Mima equation is derived as an ensemble-averaged squared Lie-Poisson bracket between two chosen functionals of the turbulent fields. The classical-limit OTOC provides a quantitative measure of how a variational perturbation applied to one functional propagates across scales in the turbulent dynamics and how it affects another functional at a later time, thereby capturing scale-dependent or field-dependent transfer processes. In a quasilinear approximation with a strong zonal flow, we derive an inverse-square decay of the OTOC with the time lag, indicating an algebraic suppression of the zonal-mode response to perturbations of the non-zonal fields. This behavior is attributed to zonal-flow shearing, which rapidly scrambles the non-zonal perturbation toward higher wavenumbers, and consequently reduces the low-wavenumber non-zonal content that can feed back onto large-scale zonal modes. |
| title | Out-of-time-ordered correlators for turbulent fields: a quantum-classical correspondence |
| topic | Plasma Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2602.21710 |