Communications in Mathematical Sciences
Volume 5 (2007)
Supplemental Issue 1
The TDHF Approximation for Hamiltonians with $m$-particle Interaction Potentials
Pages: 1 – 9
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 $(m > 2)$.
TDHF; BBGKY hierarchy; TDHF hierarchy; Slater closure; mean field dynamics; interacting fermions
2010 Mathematics Subject Classification
Primary 81V70. Secondary 47N50.