Communications in Mathematical Sciences

Volume 5 (2007)

Supp. 1

Supplemental Issue 1

The TDHF Approximation for Hamiltonians with $m$-particle Interaction Potentials

Pages: 1 – 9

DOI: http://dx.doi.org/10.4310/CMS.2007.v5.n5.a2

Authors

Claude Bardos

Bernard Ducomet

François Golse

Alex D. Gottlieb

Norbert J. Mauser

Abstract

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 $(m > 2)$.

Keywords

TDHF; BBGKY hierarchy; TDHF hierarchy; Slater closure; mean field dynamics; interacting fermions

2010 Mathematics Subject Classification

Primary 81V70. Secondary 47N50.

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