Description
Turbulent plasmas in space and laboratory are inherently multi-field, i.e., fluctuations in vorticity, density, temperature, and magnetic fields are dynamically correlated and mutually interacting. A powerful theoretical approach to reduce such complexity is known as wavekinetics, yet most established theories have focused on 1-field drift-wave models such as the Hasegawa–Mima system[1]. More recently, multi-field formulations have been proposed for ideal (nondissipative) MHD system[2], whereas the wavekinetics for multi-field systems including entropy production associated with dissipation and turbulent transport remains unexplored.
In this work, we develop a systematic derivation of wavekinetics for multi-field fluid turbulence with transport and dissipation, based on a quantum-theoretic Weyl–Wigner–Moyal formalism. As a minimal representative of multi-field system, we consider the Hasegawa–Wakatani model. By utilizing the mathematical analogy between turbulent fields and quantum states, we construct a Wigner matrix for coupled fields, and derive a corresponding Wigner–Moyal equation in phase space. The semiclassical limit yields a multi-field wavekinetic equation that consistently incorporates turbulent transport and dissipation, where the irreversible entropy production is described by von Neumann entropy[3] for the Wigner matrix. We highlight the effectiveness of decomposing the Wigner matrix into the Pauli spin-matrix basis, which maps the turbulent dynamics onto a quantum spin vector field, characterized by u(2)=u(1) ⊕ su(2) Lie-algebraic structure.
We further introduce quantum OTOC (out-of-time-ordered correlator), widely used to quantify information scrambling processes in quantum many-body physics and quantum computing, into plasma turbulence analysis[4]. Using the Weyl transform to derive the quantum-classical correspondence, the classical-limit OTOC enables the analysis of spatiotemporal correlations between perturbations and responses for arbitrary turbulent fields.
References
[1] D. E. Ruiz et al., “Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation”, J. Plasma Phys. 85, 905850101 (2019)
[2] S. Jin and I. Y. Dodin, “On reduced modelling of the modulational dynamics in magnetohydrodynamics”, J. Plasma Phys. 91, E43 (2025)
[3] G. Yatomi and M. Nakata, “von Neumann entropy of phase-space structures in gyrokinetic plasma turbulence”, Plasma Phys. Control. Fusion, in press
[4] M. Nakata, “Out-of-time-ordered correlators for turbulent fields: a quantum-classical correspondence”, Plasma Phys. Control. Fusion, in press