Classical limit for linear and nonlinear quantum Fokker-Planck systems | Zendy

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Classical limit for linear and nonlinear quantum Fokker-Planck systems

Author(s) -

Roberta Bosi

Publication year - 2009

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2009.8.845

Subject(s) - fokker–planck equation , nonlinear system , limit (mathematics) , physics , planck , convergence (economics) , classical limit , quantum , statistical physics , planck constant , mathematical analysis , mathematical physics , mathematics , quantum mechanics , partial differential equation , economics , economic growth

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 con- vergence 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.

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