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Self-consistent fluid model for a quantum electron gas

G. Manfredi·F. Haas
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Abstract

It is shown that, for a large class of statistical mixtures, the Wigner-Poisson (or Hartree) system can be reduced to an effective Schroedinger-Poisson system, in which the Schroedinger equation contains a new nonlinearity. For the case of a zero-temperature one-dimensional electron gas, this additional nonlinearity is of the form Psi^4. In the long wavelength limit, the results obtained from the effective Schroedinger-Poisson system are in agreement with those of the Wigner-Poisson system. The reduced model is further used to describe the stationary states of a quantum electron gas and the two-stream instability.

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G. Manfredi, F. Haas. 2002-03-20. Self-consistent fluid model for a quantum electron gas. https://doi.org/10.1103/physrevb.64.075316

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