Quantum breathing mode for electrons with 1/r2interaction

We show that the collective excitation spectrum of electrons with 1/${\mathit{r}}^2$ interaction in a parabolic quantum dot of frequency ${\mathrm{\omega }}_0$ contains a ‘‘breathing’’ mode of frequency 2Ω, where ${\mathrm{\Omega }}^2$≡${\mathrm{\omega }}_0^2$+1/4${\mathrm{\omega }}_{\mathit{c}}^2$ and ${\mathrm{\omega }}_{\mathit{c}}$ is the cyclotron frequency, a result first obtained by Johnson and Quiroga [Phys. Rev. Lett. 74, 4277 (1995)]. © 1996 The American Physical Society.