DERIVATION OF THE MAXWELL-SCHRODINGER EQUATIONS FROM THE PAULI-FIERZ HAMILTONIAN

Leopold, Nikolai und Pickl, Peter (2020): DERIVATION OF THE MAXWELL-SCHRODINGER EQUATIONS FROM THE PAULI-FIERZ HAMILTONIAN. In: Siam Journal on Mathematical Analysis, Bd. 52, Nr. 5: S. 4900-4936

Abstract

We consider the spinless Pauli-Fierz Hamiltonian which describes a quantum system of nonrelativistic identical particles coupled to the quantized electromagnetic field. We study its time evolution in a mean-field 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 one-body state (a Bose-Einstein 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 Maxwell-Schrodinger 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. 151-164], to condensates of charged particles in interaction with their radiation field.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0036-1410
• Sprache: Englisch