https://doi.org/10.1140/epjp/s13360-025-05995-w
Regular Article
Diffusion and turbulence in phase-space and formation of phase-space vortices
Department of Physics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, 737136, Rangpo, Sikkim, India
Received:
4
November
2024
Accepted:
8
January
2025
Published online:
13
February
2025
In this work, the recently introduced fluid-like treatment of the phase-space (Lobo and Sayal in PP 31:092301, 2024), termed as the phase-space hydrodynamic model, has been further extended, and some interesting outcomes have been presented. A modified form of the Vlasov equation has been presented, which describes the diffusion of the phase-space density. This anisotropic diffusion is analysed, and the diffusive flow of the phase-space probability field is shown. Growth of phase-space vortices is then shown due to increased turbulent-like flow, which is marked by the dominating inertial flow above the diffusive flow. The nature of this flow is judged by using a parameter for the phase-space. It is then shown that the formation of phase-space vortices is due to growth of turbulent-like flow in the phase-space. On the bases of the diffusion parameters, the vorticity field transport of the hydrodynamic phase-space is studied and a Schamel–KdV form of the vorticity transport equation is derived, suggesting solitary modes of the phase-space vorticity waves.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
