Acoustic excitations of a confined two-dimensional electron liquid in a magnetic field

We study the low-frequency excitations of a compressible electron liquid confined to a strip and subjected to a magnetic field. Using the classical equations of motion, we show the existence of gapless excitations additional to the conventional one-dimensional plasmon. These excitations are shown to have linear spectra. In contrast to the plasmon mode, the velocities of these modes increase with the magnetic field in the weak-field domain, reaching a maximum at a certain field strength. The calculated oscillator strengths and the estimate for the damping rates enable us to discuss the optimal experimental setup for the observation of the acoustic modes.