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Now plasma represents collective wave-like motions of charged particles. In 3D, their frequency is well known to be almost a constant, $\omega^{3D}_p \approx \sqrt{4\pi n e^2/m}$, with $n$=charge density, $m$=particle mass. However, in 2D, one can show that it becomes $\omega^{2D}_p \sim \sqrt{q}$, where $q$= wave number. It gets dispersion. The group velocity is then $v^{2D}_g \sim 1/\sqrt{q}$, which diverges as $q\rightarrow 0$. How could this be possible ? How could $v^{2D}_g$ exceed the speed of light, which is ridiculous to me ?

Highly appreciate your attention !!

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  • $\begingroup$ Comment to the question (v1): Consider adding references in order to receive useful and focused answers. $\endgroup$
    – Qmechanic ♦
    Commented Dec 17, 2014 at 15:12
  • $\begingroup$ Please could you give the proportionality constant which appears in $v_g^{2D}$? This should tell us at which wavelengths the group velocity approaches $c$. Presumably this is also a length scale at which the effective theory you are using becomes invalid. $\endgroup$
    – Mark Mitchison
    Commented Dec 17, 2014 at 21:40
  • $\begingroup$ Thanks for your comments. Here is a reference: rmf.smf.mx/pdf/rmf/39/4/39_4_640.pdf $\endgroup$
    – hyd
    Commented Dec 18, 2014 at 2:09
  • $\begingroup$ More precisely, $\omega^{2D}_p \approx \sqrt{2\pi ne^2/m} ~ \sqrt{q}$. There is a limit on the validity of these formula only in large $q$. $\endgroup$
    – hyd
    Commented Dec 18, 2014 at 2:10

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