Density operator approach to turbulent flows in plasma and atmospheric fluids

Abstract

We formulate a statistical wave-mechanical approach to describe dissipation and instabilities in two-dimensional turbulent flows of magnetized plasmas and atmospheric fluids, such as drift and Rossby waves. This is made possible by the existence of Hilbert space, associated with the electric potential of plasma or stream function of atmospheric fluid. We therefore regard such turbulent flows as macroscopic wave-mechanical phenomena, driven by the non-Hermitian Hamiltonian operator we derive, whose anti-Hermitian component is attributed to an effect of the environment. Introducing a wave-mechanical density operator for the statistical ensembles of waves, we formulate master equations and define observables: such as the enstrophy and energy of both the waves and zonal flow as statistical averages. We establish that our open system can generally follow two types of time evolution, depending on whether the environment hinders or assists the system's stability and integrity. We also consider a phase-space formulation of the theory, including the geometrical-optic limit and beyond, and study the conservation laws of physical observables. It is thus shown that the approach predicts various mechanisms of energy and enstrophy exchange between drift waves and zonal flow, which were hitherto overlooked in models based on wave kinetic equations.

17 pages, selected paper from the 17th Russian Gravitational Conference - International Conference on Gravitation, Cosmology and Astrophysics (RUSGRAV-17), Saint Petersburg, 28 June - 4 July 2020

References in corpus (9)

• Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems
• Wave packet evolution in non-Hermitian quantum systems
• Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
• Zonal-flow dynamics from a phase-space perspective
• Linear Quantum Entropy and Non-Hermitian Hamiltonians
• Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides
• Analytically solvable $2\times 2$ $PT$-symmetry dynamics from su(1,1)-symmetry problems
• Quasi-hermitian Quantum Mechanics in Phase Space
• Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay