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arXiv:1005.3408

Excitation of Quantized Longitudinal Electric Waves in a Degenerate Fermi Gas

Levan N. Tsintsadze

Published May 19, 2010• 0 citations
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Abstract

The system of electron beam - degenerate Fermi gas in a magnetic field is investigated. Instabilities of the quantized longitudinal electric waves are studied by a newly derived dispersion equation. Novel branches of longitudinal waves are found, which have no analogies without the Landau quantization. Growth rates of these new modes are obtained. The excitation of the zero sound by an electron beam is discussed and found that the quantization of the energy of electrons imposes a new condition. Furthermore, the excitation of Bogolyubov's type of spectrum by a strong electric field is considered.

DOI
10.48550/arxiv.1005.3408

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The system of electron beam - degenerate Fermi gas in a magnetic field is investigated. Instabilities of the quantized longitudinal electric waves are studied by a newly derived dispersion equation. Novel branches of longitudinal waves are found, which have no analogies without the Landau quantization. Growth rates of these new modes are obtained. The excitation of the zero sound by an electron beam is discussed and found that the quantization of the energy of electrons imposes a new condition. Furthermore, the excitation of Bogolyubov's type of spectrum by a strong electric field is considered.
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Abstract Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation (QKE): in the present work, propagation of waves in charged quantum gases is investigated starting from this QKE. Dispersion relations are derived for fully and weakly degenerate fermions and bosons (for the latter above critical temperature) and the differences discussed. Use of a kinetic equation permits investigation of “Landau-type” damping: it is found that the presence of damping in fermion gases is dependent upon the degree of degeneracy, whereas it is always present in boson gases. In fully degenerate fermions a phenomenon appears that is akin to the “zero sound” propagation.
The nature of spin-type zero sound, "paramagnetic spin waves" (PSW's), in free-electron gases is studied by means of the time-dependent Hartree-Fock approximation. The importance of attractive interactions is emphasized. A short-wavelength cutoff in the spectrum at microwave or low infrared frequencies is found. The effect of the application of magnetic fields is studied. The frequencies are shifted by the Larmor precession. Some branches of the spectrum are effectively eliminated; others are strengthened and split. Spin wave fronts travel in helices about magnetic field lines. PSW's are damped by electron collisions with crystal imperfections. The relaxation time is identical with the relaxation time as determined by the dc conductivity. Electron-electron collision damping is also studied and found to be negligible by comparison. The observation of Landau-damped modes is considered and conditions where this is possible are indicated. A boundary condition is found: A surface must be at an antinode of the spin density. A microwave, "thin"-film resonance experiment is suggested. The strength of the resonance lines is considered. An expression for power dissipation at PSW resonance is derived.