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The semiclassical limit
of the time dependent Hartree–Fock equation: The Weyl symbol
of the solution
Laurent Amour, Mohamed Khodja and Jean Nourrigat |
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Vol. 6 (2013), No. 7, 1649–1674
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Abstract |
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For a family of solutions to the time dependent Hartree–Fock equation, depending on the semiclassical parameter , we prove that if at the initial time the Weyl symbol of the solution is in as well as all its derivatives, then this property is true for all time, and we give an asymptotic expansion in powers of of this Weyl symbol. The main term of the asymptotic expansion is a solution to the Vlasov equation, and the error term is estimated in the norm of . |
Keywords
time dependent Hartree–Fock equation, Vlasov equation,
semiclassical analysis, Egorov theorem, pseudodifferential
operators
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Mathematical Subject Classification 2010
Primary: 35S05, 81Q20, 82C10
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Milestones
Received: 8 June 2012
Revised: 26 November 2012
Accepted: 19 January 2013
Published: 27 December 2013
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Authors |
| Laurent Amour | |
| Laboratoire de Mathématiques de
Reims Université de Reims Champagne-Ardenne EA 4535, FR CNRS-3399 51687 Reims France |
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| Mohamed Khodja | |
| Laboratoire de Mathématiques de
Reims Université de Reims Champagne-Ardenne EA 4535, FR CNRS-3399 51687 Reims France |
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| Jean Nourrigat | |
| Laboratoire de Mathématiques de
Reims Université de Reims Champagne-Ardenne EA 4535, FR CNRS-3399 51687 Reims France |
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