Linear Response Theory for a Degenerate Electron Gas in a Strong Magnetic Field

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Abstract
The complete quantum-mechanical response of an electron gas in the presence of a strong dc magnetic field is discussed. The effect of collisions of the electrons with impurities and lattice imperfections is accounted for by means of a single relaxation time. In addition to the conduction current, a diffusion current associated with spatial variations in the electron density and a collision drag current for the case of acoustic propagation are evaluated. The results are expressed in a form quite analogous to the semiclassical result and convenient for studying quantum effects in the case of small-wavelength disturbances. A formal application of the results to the problem of acoustic propagation and to the diamagnetic interaction among the conduction electrons is presented. A number of useful sum rules and mathematical results are derived in appendices.

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