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February 2007 The TDHF Approximation for Hamiltonians with $m$-particle Interaction Potentials
Claude Bardos, Bernard Ducomet, François Golse, Alex D. Gottlieb, Norbert J. Mauser
Commun. Math. Sci. 5(S1): 1-9 (February 2007).


According to a theory of H. Spohn, the time-dependent Hartree (TDH) equation governs the 1-particle state in $N$-particle systems whose dynamics are prescribed by a non-relativistic Schrödinger equation with 2-particle interactions, in the limit $N$ tends to infinity while the strength of the 2-particle interaction potential is scaled by $1=N$. In previous work we have considered the same mean field scaling for systems of fermions, and established that the error of the time-dependent Hartree-Fock (TDHF) approximation tends to 0 as $N$ tends to infinity. In this article we extend our results to systems of fermions with m-particle interactions $(m > 2)$.


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Claude Bardos. Bernard Ducomet. François Golse. Alex D. Gottlieb. Norbert J. Mauser. "The TDHF Approximation for Hamiltonians with $m$-particle Interaction Potentials." Commun. Math. Sci. 5 (S1) 1 - 9, February 2007.


Published: February 2007
First available in Project Euclid: 5 April 2007

zbMATH: 1135.81385
MathSciNet: MR2301285

Primary: 81V70
Secondary: 47N50

Keywords: BBGKY hierarchy , interacting fermions , mean field dynamics , Slater closure , TDHF , TDHF hierarchy

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. S1 • February 2007
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