Norm approximation for the Fröhlich dynamics in the mean-field regime

Leopold, Nikolai

doi:10.1016/j.jfa.2023.109979

Cited by 2 publications

(2 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, the regularized Nelson model was studied also in a many-fermion limit that is closely linked to a semiclassical limit [62]. Other particle-field systems, such as the Fröhlich model and the Pauli-Fierz Hamiltonian, have been studied in the scaling regime of the present article too, see [61,64] for the mean-field approximation and [59] for an approximation of the Fröhlich dynamics in norm. The dressed Nelson Hamiltonan, which will play a crucial role in our analysis (see Section 1.4), has similar regularity properties to the Fröhlich Hamiltonian, as both are given in terms of perturbations of the non-interacting quadratic form.…”

Section: 3mentioning

confidence: 99%

See 1 more Smart Citation

Bogoliubov dynamics and higher-order corrections for the regularized Nelson model

et al. 2023

View full text Add to dashboard Cite

We study the time evolution of the Nelson model in a mean-field limit in which [Formula: see text] nonrelativistic bosons weakly couple (with respect to the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of partial differential equations describing the time evolution of the first- and second-order approximations to the one-particle reduced density matrices of the particles and the quantum field, respectively.

show abstract

Section: 3mentioning

confidence: 99%

“…Equipped with these estimates we can now come to the proof of Theorem 3.2, whose strategy is inspired by [15,59,76].…”

Section: Mean-field Approximation Of the Dressed Dynamics Given The D...mentioning

confidence: 99%

Bogoliubov dynamics and higher-order corrections for the regularized Nelson model

et al. 2023

View full text Add to dashboard Cite

show abstract

Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field

Falconi

Leopold

2023

Journal of Mathematical Physics

View full text Add to dashboard Cite

We slightly extend prior results about the derivation of the Maxwell–Schrödinger equations from the bosonic Pauli–Fierz Hamiltonian. More concretely, we show that the findings from Leopold and Pickl [SIAM J. Math. Anal. 52(5), 4900–4936 (2020)] about the coherence of the quantized electromagnetic field also hold for soft photons with small energies. This is achieved with the help of an estimate from Ammari et al. [arXiv:2202.05015 (2022)], which proves that the domain of the number of photon operator is invariant during the time evolution generated by the Pauli–Fierz Hamiltonian.

show abstract

Norm approximation for the Fröhlich dynamics in the mean-field regime

Cited by 2 publications

References 35 publications

Bogoliubov dynamics and higher-order corrections for the regularized Nelson model

Bogoliubov dynamics and higher-order corrections for the regularized Nelson model

Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field

Contact Info

Product

Resources

About