dorsal/arxiv
View SchemaHow to model quantum plasmas
| Authors | G. Manfredi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505004 |
| URL | https://arxiv.org/abs/quant-ph/0505004 |
Abstract
Traditional plasma physics has mainly focused on regimes characterized by high temperatures and low densities, for which quantum-mechanical effects have virtually no impact. However, recent technological advances (particularly on miniaturized semiconductor devices and nanoscale objects) have made it possible to envisage practical applications of plasma physics where the quantum nature of the particles plays a crucial role. Here, I shall review different approaches to the modeling of quantum effects in electrostatic collisionless plasmas. The full kinetic model is provided by the Wigner equation, which is the quantum analog of the Vlasov equation. The Wigner formalism is particularly attractive, as it recasts quantum mechanics in the familiar classical phase space, although this comes at the cost of dealing with negative distribution functions. Equivalently, the Wigner model can be expressed in terms of $N$ one-particle Schr{\"o}dinger equations, coupled by Poisson's equation: this is the Hartree formalism, which is related to the `multi-stream' approach of classical plasma physics. In order to reduce the complexity of the above approaches, it is possible to develop a quantum fluid model by taking velocity-space moments of the Wigner equation. Finally, certain regimes at large excitation energies can be described by semiclassical kinetic models (Vlasov-Poisson), provided that the initial ground-state equilibrium is treated quantum-mechanically. The above models are validated and compared both in the linear and nonlinear regimes.
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"abstract": "Traditional plasma physics has mainly focused on regimes characterized by\nhigh temperatures and low densities, for which quantum-mechanical effects have\nvirtually no impact. However, recent technological advances (particularly on\nminiaturized semiconductor devices and nanoscale objects) have made it possible\nto envisage practical applications of plasma physics where the quantum nature\nof the particles plays a crucial role. Here, I shall review different\napproaches to the modeling of quantum effects in electrostatic collisionless\nplasmas. The full kinetic model is provided by the Wigner equation, which is\nthe quantum analog of the Vlasov equation. The Wigner formalism is particularly\nattractive, as it recasts quantum mechanics in the familiar classical phase\nspace, although this comes at the cost of dealing with negative distribution\nfunctions. Equivalently, the Wigner model can be expressed in terms of $N$\none-particle Schr{\\\"o}dinger equations, coupled by Poisson\u0027s equation: this is\nthe Hartree formalism, which is related to the `multi-stream\u0027 approach of\nclassical plasma physics. In order to reduce the complexity of the above\napproaches, it is possible to develop a quantum fluid model by taking\nvelocity-space moments of the Wigner equation. Finally, certain regimes at\nlarge excitation energies can be described by semiclassical kinetic models\n(Vlasov-Poisson), provided that the initial ground-state equilibrium is treated\nquantum-mechanically. The above models are validated and compared both in the\nlinear and nonlinear regimes.",
"arxiv_id": "quant-ph/0505004",
"authors": [
"G. Manfredi"
],
"categories": [
"quant-ph"
],
"title": "How to model quantum plasmas",
"url": "https://arxiv.org/abs/quant-ph/0505004"
},
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