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Quantum breathing mode for electrons with 1/<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">r</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>interaction
We show that the collective excitation spectrum of electrons with 1/${\mathit{r}}^{2}$ interaction in a parabolic quantum dot of frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ contains a ``breathing'' mode of frequency 2\ensuremath{\Omega}, where ${\mathrm{\ensuremath{\Omega}}}^{2}$\ensuremath{\equiv}${\mathrm{\ensuremath{\omega}}}_{0}^{2}$+1/4${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}^{2}$ and ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ is the cyclotron frequency, a result first obtained by Johnson and Quiroga [Phys. Rev. Lett. 74, 4277 (1995)]. \textcopyright{} …