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

TL;DR

This paper models bosons interacting with a quantized photon field, deriving nonlinear cascade equations that demonstrate the dynamic formation of a Bose-Einstein condensate through energy flow, distinct from thermal relaxation.

Contribution

It introduces a novel nonlinear cascade framework for boson-photon interactions in mean field QED, explaining dynamic BEC formation beyond thermal processes.

Findings

Nonlinear cascade equations govern photon emission and absorption.

Energy flow in bosons decreases monotonically, leading to BEC formation.

The process is fundamentally nonlinear and different from thermal relaxation.

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 describe a monotone decreasing energy flow in the boson subsystem. Thereby, we prove that a Bose-Einstein condensate (BEC) forms dynamically, 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.