I review results concerning the derivation of effective equations for the dynamics of interacting Fermi gases in a high-density regime of mean-field type. Three levels of effective theories, increasing in precision, can be distinguished: the semiclassical theory given by the Vlasov equation, the mean-field theory given by the Hartree–Fock equation, and the description of the dominant effects of non-trivial entanglement by the random phase approximation. Particular attention is given to the discussion of admissible initial data, and I present an example of a realistic quantum quench that can be approximated by Hartree–Fock dynamics.
Effective dynamics of interacting fermions from semiclassical theory to the random phase approximation
Note: This paper is part of the Special Collection: XX International Congress on Mathematical Physics.
Niels Benedikter; Effective dynamics of interacting fermions from semiclassical theory to the random phase approximation. J. Math. Phys. 1 August 2022; 63 (8): 081101. https://doi.org/10.1063/5.0091694
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