# Mean-Field Dynamics for the Nelson Model with Fermions

@article{Leopold2019MeanFieldDF, title={Mean-Field Dynamics for the Nelson Model with Fermions}, author={Nikolai Leopold and Soren Petrat}, journal={Annales Henri Poincar{\'e}}, year={2019} }

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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