Trapped bosons in mean field QED, nonlinear resonance cascades and dynamical BEC formation

Abstract

In this paper, we study a system of bosons trapped in a confining potential, interacting with a quantized field of coherent photons in the mean field description of non-relativistic Quantum Electrodynamics (QED) obtained by [N. Leopold and P. Pickl , 2017]. We derive the effective nonlinear cascade equations governing the emission and absorption of coherent photons by the boson subsystem in a combined weak-coupling and macroscopic time limit. We demonstrate that solutions to this nonlinear cascade determine a monotone decreasing energy flow in the boson subsystem, and thereby describe the dynamical formation of a Bose-Einstein condensate (BEC) with full ground state occupation, under conservation of the total boson $L^2$ mass. We note that this process is crucially different from thermal relaxation to the ground state, and fundamentally depends on the nonlinear nature of the cascade dynamics.

AMS Latex, 64 pages. Significantly revised and corrected version. Diophantine condition added, and macroscopic time domain extended to R_+