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Quantum hydrodynamics for plasmas—Quo vadis?

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Bonitz, M., Moldabekov, Zh. A., Ramazanov, T. S.·2019·Physics of Plasmas
DOI 10.1063/1.5097885
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Abstract

Quantum plasmas are an important topic in astrophysics and high pressure laboratory physics for more than 50 years. In addition, many condensed matter systems, including the electron gas in metals, metallic nanoparticles, or electron-hole systems in semiconductors and heterostructures, exhibit—to some extent—plasmalike behavior. Among the key theoretical approaches that have been applied to these systems are quantum kinetic theory, Green function theory, quantum Monte Carlo, semiclassical and quantum molecular dynamics, and more recently, density functional theory simulations. These activities are in close contact with the experiments and have firmly established themselves in the fields of plasma physics, astrophysics, and condensed matter physics. About two decades ago, a second branch of quantum plasma theory emerged that is based on a quantum fluid description and has attracted a substantial number of researchers. The focus of these studies has been on collective oscillations and linear and nonlinear waves in quantum plasmas. Even though these papers pretend to address the same physical systems as the more traditional papers mentioned above, the former appear to form a rather closed community that is largely isolated from the rest of the field. The quantum hydrodynamics (QHD) results have—with a few exceptions—not found application in astrophysics or in experiments in condensed matter physics. Moreover, these results practically did not have any impact on the former quantum plasma theory community. One reason is the unknown accuracy of the QHD for dense plasmas. In this paper, we present a novel derivation, starting from reduced density operators that clearly point to the deficiencies of QHD, and we outline possible improvements. It is also to be noted that some of the QHD results have attracted negative attention being criticized as unphysical. Examples include the prediction of “novel attractive forces” between protons in an equilibrium quantum plasma, the notion of “spinning quantum plasmas,” or the new field of “quantum dusty plasmas.” In the present article, we discuss the latter system in some detail because it is a particularly disturbing case of formal theoretical investigations that are detached from physical reality despite bold and unproven claims of importance for, e.g., dense astrophysical plasmas or microelectronics. We stress that these deficiencies are not a problem of QHD itself, which is a powerful and efficient method, but rather are due to ignorance of its properties and limitations. We analyze the common flaws of these works and come up with suggestions to improve the situation of QHD applications to quantum plasmas.

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  • Several improved quantum hydrodynamical models have been put forward in the recent literature.

    “Note, however, that several improved quantum hydrodynamical models have been put forward in the recent literature; see, e.g., Refs.(Moldabekov et al. 2018;Bonitz et al. 2019;Manfredi et al. 2021).”

    From Quantum kinetic theory of plasmas (2022) · cites this paper as Bonitz et al. 2019

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Authors
Bonitz, M., Moldabekov, Z. A., & Ramazanov, T. S.
Affiliations
  • Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel 1 , Leibnizstraße 15, 24098 Kiel, Germany
  • Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University 2 , 71 Al-Farabi Str., 050040 Almaty, Kazakhstan
ORCID
Venue
Physics of Plasmas
Publisher
AIP Publishing
Published
2019-09-01
Volume
26
Issue
9
ISSN
  • 1070-664X (ISSN-L)
  • 1089-7674
DOI
10.1063/1.5097885
OpenAlex
W2972962971
Cited by
110
References
196
Citations by year
2026: 5 · 2025: 15 · 2024: 15 · 2023: 17 · 2022: 16 · 2021: 18 · 2020: 22 · 2019: 2
FWCI
6.38
Type
journal article
Language
en
Open access
Licence
Locations
Physics of Plasmas (publishedVersion, cc-by)
Funders
  • Deutsche Forschungsgemeinschaft (BO1366/13)
  • Deutscher Akademischer Austauschdienst
  • Ministry of Education and Science of the Republic of Kazakhstan (BR05236730)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Dust and Plasma Wave Phenomena
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Laser-Plasma Interactions and Diagnostics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Magnetic confinement fusion research
Keywords
quantum hydrodynamics, quantum plasma, reduced density operator, collective oscillations, nonlinear waves, quantum dusty plasma, high-density plasma, electron-hole systems, metal nanoparticles

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