A plasma is regarded as quantum if its macroscopic properties are significantly affected by the quantum nature of its constituent particles. A proper description is necessary to comprehend when collective quantum plasma effects are important. In this paper, the most commonly used microscopic approaches to describe a collisionless quantum plasma are reviewed, together with their related assumptions and restrictions. In particular, the quantum plasma hydrodynamic approximation is analyzed in detail, and the analytical properties of the linear dielectric response function obtained from quantum plasma kinetic theory are investigated. Special attention is paid to what we consider to be the most important problems that have already appeared in the linear approximation and require further studies.

PACS: 05.30.Fk, 52.25.−b, 52.35.−g (all) DOI: 10.3367/UFNe.0181.201112g.1313 URL: https://ufn.ru/en/articles/2011/12/c/ 000303761500003 2011PhyU...54.1243V Citation: Vladimirov S V, Tyshetskiy Yu O "On description of a collisionless quantum plasma" Phys. Usp. 54 1243–1256 (2011) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 21st, December 2010, revised: 23rd, May 2011, accepted: 23rd, May 2011 Оригинал: Владимиров С В, Тышецкий Ю О «Об описании бесстолкновительной квантовой плазмы» УФН 181 1313–1328 (2011); DOI: 10.3367/UFNr.0181.201112g.1313