Bosonization of Fermionic Many-Body Dynamics

@article{Benedikter2021BosonizationOF,
  title={Bosonization of Fermionic Many-Body Dynamics},
  author={Niels Benedikter and Phan Th{\`a}nh Nam and Marcello Porta and Benjamin Schlein and Robert Seiringer},
  journal={Annales Henri Poincar{\'e}},
  year={2021}
}
We consider the quantum many–body evolution of a homogeneous Fermi gas in three dimensions in the coupled semiclassical and mean-field scaling regime. We study a class of initial data describing collective particle–hole pair excitations on the Fermi ball. Using a rigorous version of approximate bosonization, we prove that the many–body evolution can be approximated in Fock space norm by a quasifree bosonic evolution of the collective particle–hole excitations. 

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