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Mean-field Dynamics for the Nelson model with Fermions

Date: Thursday, February 1, 2018 16:00 - 18:00
Speaker: Nikolai Leopold (IST Austria)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Formal Sciences Seminar
Host: Robert Seiringer
Lab building west seminar room


The Nelson model (with ultraviolet cutoff) describes a quantum system of non-relativistic identical particles coupled to a quantized scalar field. In this talk, I would like to discuss its time evolution in a mean-field limit of many fermions which is coupled to a semiclassical limit. At time zero, we assume that the gauge bosons of the radiation field are in a coherent state and that the state of the fermions is given by a Slater determinant, whose reduced one-particle density matrix is an orthogonal projection with semiclassical structure. I will motivate that at later times and in the limit of many fermions it can be proven that the fermion state remains close to a slater determinant and that the time evolution is approximately described by the fermionic Schrödinger-Klein-Gordon equations. I will introduce the mentioned models and discuss the status and the structure of the proof. The talk reports about work in progress with Sören Petrat.

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