Electron-phonon energy relaxation in quasi-one-dimensional electron systems in zero and quantizing magnetic fields

The nature of the acoustic-phonon emission from a quasi-one-dimensional electron gas has been shown to vary with electron temperature ${\mathit{T}}_{\mathit{e}}$ and confinement potential. Intensity oscillations occur as the one-dimensional levels are moved through the Fermi level ${\mathit{E}}_{\mathit{F}}$ and quasimonochromatic phonons are emitted at higher temperatures. Analytical expressions have been obtained for the frequency spectrum of the total energy-loss rate Q and very marked changes with ${\mathit{T}}_{\mathit{e}}$ are predicted in the angular distribution of emitted phonons. The emission is strongly affected by magnetic field. At low ${\mathit{T}}_{\mathit{e}}$, oscillatory behavior of Q at relatively low field is replaced by a monotonic increase followed by a sharp fall when the Fermi velocity drops below the velocity of sound. Marked changes should also occur in the angular distribution.