This seminar concludes Prof. Pickl's graduate course "Manybody quantum dynamics and nonlinear effective evolution equations" and focuses on the generalisation of Pickl's "counting method" to systems in interaction with a secondquantised radiation field. First, we introduce the Nelson model with cutoff, which describes a quantum system of nonrelativistic particles coupled to a massive (or massless) scalar Bose field. We study the time evolution in a meanfield limit where the number N of charged particles becomes large while the coupling with the radiation field is rescaled by N^{1/2}. At time zero we assume that almost all particles are in the same onebody state (a BoseEinstein condensate) and we assume also that the Bose excitations of the radiation field are not present (vacuum state) or are close to a coherent state. We then show that at later times and in the limit N → ∞ the charged particles remain in a BoseEinstein condensate, with the time evolution approximatively described by a Schroedinger + KleinGordon system of equations, which models the coupling of a nonrelativistic particle to a classical KleinGordon field. Afterwards, we shall explain how the proof can be modified so as to derive the Hartree + Maxwell system of equations from the the manybody PauliFierz Hamiltonian.
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Meanfield limits of charged particles in interaction with their radiation field
Research Group:
Speaker:
Nikolai Leopold
Institution:
LMU Munich
Schedule:
Friday, March 11, 2016  16:00
Location:
A136
Abstract:
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