Dynamical BEC formation and vanishing entropy for trapped bosons in non-relativistic QED via nonlinear resonance cascades
Abstract
The dynamical formation of a complete Bose-Einstein condensate and the asymptotic purification of trapped bosons coupled to a quantized radiation field are rigorously established. By tracking the macroscopic one-particle density matrix κT through a nonlinear resonance cascade, it is demonstrated that radiative relaxation irreversibly depletes all excited trap modes, even when the initial macroscopic state κ0 is genuinely mixed. Here κT is an average, with respect to a de Finetti measure μ0, over mean-field particle-field orbits, so that the mixedness of κ0 reflects a statistical ensemble of orbits. Under the assumptions of a non-vanishing initial ground state component and strictly positive downward Fermi-Golden-Rule rates, strong trace-norm convergence to a pure condensate is proven, limT→∞ | κT−|χ0⟩⟨χ0| |S1(h) = 0 . Furthermore, the von Neumann entropy of the macroscopic one-particle density matrix is shown to vanish asymptotically, limT→∞S[κT]=0 , without any claim of monotonicity in T. Thus, any initially mixed, positive-entropy state (0<S[κ0]<∞) is purified to the ground state |χ0⟩⟨χ0|. For the proof, we derive the Hartree hierarchy of the coupled system of bosons and photons from the finite-N BBGKY hierarchy of the microscopic quantum many-body system, establishing trace-norm convergence in the mean-field limit as N→∞. The limits are taken successively; first N→∞, then the weak-coupling limit, and finally T→∞. Although the global particle-field evolution remains unitary, the macroscopic one-particle state converges to a pure state as energy and correlations are continuously radiated into the dispersive field.
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BibTeX
@misc{chen2026dynamical,
title = {{Dynamical BEC formation and vanishing entropy for trapped bosons in non-relativistic QED via nonlinear resonance cascades}},
author = {Thomas Chen and Ali Mezher},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17923},
eprint = {2610.17923},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17923},
}
RIS
TY - UNPB
TI - Dynamical BEC formation and vanishing entropy for trapped bosons in non-relativistic QED via nonlinear resonance cascades
AU - Thomas Chen
AU - Ali Mezher
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17923
UR - https://arxiv.org/abs/2610.17923
AB - The dynamical formation of a complete Bose-Einstein condensate and the asymptotic purification of trapped bosons coupled to a quantized radiation field are rigorously established. By tracking the macroscopic one-particle density matrix κ_T through a nonlinear resonance cascade, it is demonstrated that radiative relaxation irreversibly depletes all excited trap modes, even when the initial macroscopic state κ_0 is genuinely mixed. Here κ_T is an average, with respect to a de Finetti measure μ_0, over mean-field particle-field orbits, so that the mixedness of κ_0 reflects a statistical ensemble of orbits. Under the assumptions of a non-vanishing initial ground state component and strictly positive downward Fermi-Golden-Rule rates, strong trace-norm convergence to a pure condensate is proven, lim_T→∞ | κ_T−|χ_0⟩⟨χ_0| |_S_1(h) = 0 . Furthermore, the von Neumann entropy of the macroscopic one-particle density matrix is shown to vanish asymptotically, lim_T→∞S[κ_T]=0 , without any claim of monotonicity in T. Thus, any initially mixed, positive-entropy state (0<S[κ_0]<∞) is purified to the ground state |χ_0⟩⟨χ_0|. For the proof, we derive the Hartree hierarchy of the coupled system of bosons and photons from the finite-N BBGKY hierarchy of the microscopic quantum many-body system, establishing trace-norm convergence in the mean-field limit as N→∞. The limits are taken successively; first N→∞, then the weak-coupling limit, and finally T→∞. Although the global particle-field evolution remains unitary, the macroscopic one-particle state converges to a pure state as energy and correlations are continuously radiated into the dispersive field.
ER -