Lucas Jougla | Searcharxiv

arXiv2026

Classical limit of the Pauli-Fierz dynamics

We study the Schr\"odinger evolution generated by the Pauli-Fierz Hamiltonian, a model for nonrelativistic quantum electrodynamics, in the classical limit $\hbar \rightarrow 0$. In this regime, we rigorously derive the Newton-Maxwell equations of classical electrodynamics as effective dynamics approximating the time evolution. Our result complements prior work by an alternative derivation that provides explicit estimates on the rate of convergence, justifying the validity of the approximation for a special class of initial data.

math-ph↗

arXiv2025

$\Phi^4_2$ theory limit of a many-body bosonic free energy

We consider the quantum Gibbs state of an interacting Bose gas on the 2D torus. We set temperature, chemical potential and coupling constant in a regime where classical field theory gives leading order asymptotics. In the same limit, the repulsive interaction potential is set to be short-range: it converges to a Dirac delta function with a rate depending polynomially on the other scaling parameters. We prove that the free-energy of the interacting Bose gas (counted relatively to the non-interacting one) converges to the free energy of the $\Phi^4_2$ non-linear Schr\"odinger-Gibbs measure, thereby revisiting recent results and streamlining proofs thereof. We combine the variational method of Lewin-Nam-Rougerie to connect, with controled error, the quantum free energy to a classical Hartree-Gibbs one with smeared non-linearity. The convergence of the latter to the $\Phi^4_2$ free energy then follows from arguments of Fr\"ohlich-Knowles-Schlein-Sohinger. This derivation parallels recent results of Nam-Zhu-Zhu.

math.AP↗