Self-consistent fluid model for a quantum electron gas

By Giovanni Manfredi, F. Haas. 2001

591 citations recorded by the source corpus.

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 vertical bar {Psi} vertical bar{sup 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.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4f5dd589bff8422ac38ed1b23741a824f10baf78

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Theoretical foundations of quantum hydrodynamics for plasmas (2017, methodology): “(2), m ∂ ∂t j (r, t)− n (r, t) eE(r, t) = −∇PF [n(r, t)]− n (r, t)∇VB [n(r, t)], (3) Manfredi and Haas [31] derived the Fermi pressure and a quantum correction in the form of the Bohm potential using a semi-classical Hartree ansatz for the N -electron wave functions with identical amplitude for all ”
Ab initio simulation of warm dense matter (2019, background): “Quantum hydrodynamics (QHD) models for dense plasmas have experienced high activity since the work of Manfredi and Haas [85, 86].”
Colloquium : nonlinear collective interactions in quantum plasmas with degenerate electron fluids (2010, methodology): “The non-relativistic QHD equations (Wilhelm, 1971) have been developed in condensed matter physics (Gardner and Ringhofer, 1996) and in plasma physics (Manfredi, 2005; Manfredi and Haas, 2001).”
Quantum Hydrodynamics (2013, methodology): “However, the e−e collision rate (inverse of the electron lifetime τee) is controlled by the process of Pauli blocking [46].”
Second- and third-harmonic generation in metal-based structures (2010, methodology): “It is interesting and equally instructive to also look at a quantum model of the pressure [54].”
How to model quantum plasmas (2005, background): “equations were derived in [29].”