On the periodic Wigner--Poisson--Fokker--Planck system (Q1856913)
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scientific article; zbMATH DE number 1866683
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the periodic Wigner--Poisson--Fokker--Planck system |
scientific article; zbMATH DE number 1866683 |
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On the periodic Wigner--Poisson--Fokker--Planck system (English)
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11 February 2003
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The aim of this paper is the analysis of the coupled Wigner-Poisson-Fokker-Planck (WPFP) system in one dimension with periodic boundary conditions in the spatial direction. The existence and uniqueness of global classical solutions is analyzed. The main technical difficulty in the existence proof is to show that the quantum Fokker-Planck term is a semigroup-generator in a weighted \(L^2\)-space. The potential term is then a Lipschitz perturbation of it.
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Wigner equation
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Fokker-Planck equation
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diffusive quantum systems
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semigroup theory
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