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Mean field dynamics of fermions and the time-dependent Hartree-Fock equation. (English) Zbl 1029.82022
Summary: The time-dependent Hartree-Fock equations are derived from the \(N\)-body linear Schrödinger equation with the mean-field scaling in the limit \(N\to +{\infty}\) and for initial data that are close to Slater determinants. Only the case of bounded, symmetric binary interaction potentials is treated in this work. We prove that, as \(N\to +{\infty}\), the first partial trace of the \(N\)-body density operator approaches the solution of the time-dependent Hartree-Fock equations (in operator form) in the sense of the trace norm.

82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
82C22 Interacting particle systems in time-dependent statistical mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
47N50 Applications of operator theory in the physical sciences
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