ELECTRON CONDUCTIVITY IN HIGH MAGNETIC FIELDS BY TEST-PARTICLE TECHNIQUE

The test-particle formalism of Rostoker is applied to electrons which move only in one dimension through randomly distributed, singly charged ions. This model is appropriate to the limit of infinite magnetic field. The test particle equations are solved to find the conductivity σ(k→,ω) for arbitrary wave number k→, neglecting electron-electron correlations. In the long-wavelength limit k→=0 our result agrees with previous work. We then find explicit expressions for σ(ω), using degenerate statistics for the electrons. Contributions emerge both from excitation of undamped normal modes and from nonresonant individual particle scattering. For finite magnetic fields the cyclotron motion of the electrons is important, and we explicitly analyze the corrections to the one-dimensional model when ω is comparable to ωc. Further corrections for higher frequencies or lower magnetic fields may be obtained by a straightforward procedure. © 1969 The American Physical Society.