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arXiv · 1807.06781

Mean-field Dynamics for the Nelson Model with Fermions

Nikolai Leopold·Sören Petrat
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Abstract

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 with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schroedinger-Klein-Gordon equations.

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Nikolai Leopold, Sören Petrat. 2019-07-13. Mean-field Dynamics for the Nelson Model with Fermions. https://doi.org/10.1007/s00023-019-00828-w

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