New Dust Modes in Quantum Dusty Plasmas
L. Stenflo∗, P. K. Shukla∗ and M. Marklund∗
∗Department of Physics, Umeå University, SE–901 87 Umeå, Sweden
Abstract. The existence of two new low-frequency electrostatic modes in quantum dusty plasmas is pointed out. These modes
can be useful to diagnose charged dust impurities in micro-electro-mechanical systems.
Keywords: Quantum plasma, dusty plasma, plasma oscillations
PACS: 52.27.Lw, 52.35.Fp, 03.65.-w
Recently, there has been a great deal of interest in investigating high- and low-frequency electrostatic modes [1, 2, 3, 4, 5, 6]
in an unmagnetized quantum plasma. For this purpose, the authors of Refs.  and [3, 4, 5] have used quantum transport
models for the electrons and ions, and derived modified dispersion relations for Langmuir and ion-acoustic waves. However, in
micro-electro-mechanical systems  one also encounters high-Z charged dust impurities , which can affect the system. As a
consequence, we expect that ultra-cold quantum plasmas can support new dust modes . Examples of such quantum plasmas,
as well as the range of validity of their existence, has been discussed recently in Ref. .
Let us consider a three component quantum plasma containing electrons, ions, and charged dust impurities with unperturbed
number densities ne0, ni0, and nd0, respectively. At equilibrium, we have Zini0 = ne0 +eZdnd0, where Zi is the ion charge
state, e = 1(−1) for negatively (positively) charged dust particles, and Zd is the number of electrons/ions residing on the dust
particulates.We assume that the latter are charged electrostatically. In the presence of an electrostatic field E = −Ñf , where f is
the electrostatic potential, the electron density perturbation ne1 (≪ne0) in quantum plasmas is given by On the other hand, in the opposite limit Kq ≪(kkDi)1/2, Eq. (13) gives the usual dust acoustic wave frequency  kCD, where
CD =wpd/kDi is the dust acoustic speed.
To summarize, we have presented the dispersion properties of two new low-frequency electrostatic modes in an unmagnetized
quantum dusty plasma. The new modes are associated with the inertia of the ions and dust impurities, as well as with a force
caused by the quantumcorrelations of the electron number density fluctuations that balance the electrostatic force. The frequency
spectra of these modes should be useful in investigations of the charge density of dust impurities in micro-electro-mechanical
This research was partially supported by the Swedish Research Council and the Deutsche Forschungsgemeinschaft (Bonn).
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