Mean-Field Dynamics for the Nelson Model with Fermions

  title={Mean-Field Dynamics for the Nelson Model with Fermions},
  author={Nikolai Leopold and Soren Petrat},
  journal={Annales Henri Poincar{\'e}},
We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant… 
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