Leopold, Nikolai; Pickl, Peter
(2020):
DERIVATION OF THE MAXWELLSCHRODINGER EQUATIONS FROM THE PAULIFIERZ HAMILTONIAN.
In: Siam Journal on Mathematical Analysis, Vol. 52, No. 5: pp. 49004936

Full text not available from 'Open Access LMU'.
Abstract
We consider the spinless PauliFierz Hamiltonian which describes a quantum system of nonrelativistic identical particles coupled to the quantized electromagnetic field. We study its time evolution in a meanfield limit where the number N of charged particles gets large while the coupling to the radiation field is rescaled by 1/root N. At time zero we assume almost all charged particles to be in the same onebody state (a BoseEinstein condensate) and the photons to be close to a coherent state. In the limit N > infinity we show that the time evolution preserves the condensate as well as the coherent structure and that it can be approximated by the MaxwellSchrodinger system, which models the coupling of a nonrelativistic particle to the classical electromagnetic field. Our result is obtained by an extension of the method of counting, introduced in [P. Pickl, Lett. Math. Phys., 97 (2011), pp. 151164], to condensates of charged particles in interaction with their radiation field.