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Asymptotically exact dispersion relations for collective modes in a confined charged Fermi liquid

Asymptotically exact dispersion relations for collective modes in a confined charged Fermi liquid

Using general local conservation laws we derive dispersion relations for edge modes in a slab of electron liquid confined by a symmetric potential. The dispersion relations are exact up to ${\ensuremath{\lambda}}^{2}{q}^{2},$ where q is a wave vector and $\ensuremath{\lambda}$ is an effective screening length. For a harmonic external potential the …