Classical limit for linear and nonlinear quantum Fokker-Planck systems

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May 2009, 8(3): 845-870. doi: 10.3934/cpaa.2009.8.845

Classical limit for linear and nonlinear quantum Fokker-Planck systems

1.	Institut für Analysis und Scientific Computing, Wiedner Hauptstr. 8, A 1040 Wien, Österreich

Received March 2008 Revised December 2008 Published February 2009

Abstract
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We study the classical limit of some linear and nonlinear Quantum Fokker-Planck systems. In the nonlinear case we consider an Hartree-type potential. By the use of the Wigner transform and compactness methods, we prove the convergence of the system to a linear and nonlinear Vlasov Fokker- Planck equation respectively. The physical case with a Poisson coupling in three dimensions is included.

Keywords: Fokker-Planck operator, quantum transport, Classical limit, Hartree equation, Wigner measure, open quantum system..

Mathematics Subject Classification: 81Q15, 82C10, 35Q40, 35S10, 47J35, 47H06, 47H20, 81V70, 81Q99, 81V9.

Citation: Roberta Bosi. Classical limit for linear and nonlinear quantum Fokker-Planck systems. Communications on Pure & Applied Analysis, 2009, 8 (3) : 845-870. doi: 10.3934/cpaa.2009.8.845

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