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The TDHF approximation for Hamiltonians with \(m\)-particle interaction potentials. (English) Zbl 1135.81385

Summary: 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 \((m> 2)\).

MSC:

81V70 Many-body theory; quantum Hall effect
47N50 Applications of operator theory in the physical sciences
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