# American Institute of Mathematical Sciences

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

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.
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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