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 Schrödinger–Klein–Gordon equations.
Annales Henri Poincare
Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. 2019;20(10):3471–3508. doi:10.1007/s00023-019-00828-w
Leopold, N. K., & Petrat, S. P. (2019). Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare, 20(10), 3471–3508. https://doi.org/10.1007/s00023-019-00828-w
Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” Annales Henri Poincare 20, no. 10 (2019): 3471–3508. https://doi.org/10.1007/s00023-019-00828-w.
N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model with fermions,” Annales Henri Poincare, vol. 20, no. 10, pp. 3471–3508, 2019.
Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. 20(10), 3471–3508.
Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” Annales Henri Poincare, vol. 20, no. 10, Springer Nature, 2019, pp. 3471–3508, doi:10.1007/s00023-019-00828-w.
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