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This theoretical study establishes a rigorous mathematical framework demonstrating how a Bose-Einstein condensate forms dynamically through nonlinear resonance cascades in mean-field QED, distinct from standard thermal relaxation. By deriving effective cascade equations that describe monotone energy flow in a weak-coupling limit, the work provides fundamental insights into the interplay between bosonic subsystems and coherent photon fields. The results advance the analytical understanding of dynamical condensation processes, offering a precise model for energy dissipation in trapped boson systems without relying on thermal equilibrium assumptions.
Trapped bosons in mean field QED, nonlinear resonance cascades and dynamical BEC formation
arXiv:2604.11756v3 Announce Type: replace-cross 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.
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.
AMS Latex, 56 pages. Typos corrected, added Remark 1.1, Remark 1.3, and acknowledgments
Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Quantum Physics (quant-ph)
arXiv:2604.11756 [math-ph]
(or arXiv:2604.11756v3 [math-ph] for this version)
Full text under the publisher's open licence · 161 words
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