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 / N. Benedikter. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 63:8(2022 Aug), pp. 081101.1-081101.17. [10.1063/5.0091694]
Effective dynamics of interacting fermions from semiclassical theory to the random phase approximation
N. Benedikter
2022
Abstract
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.File | Dimensione | Formato | |
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