PreprintCC BY 4.0arXiv
Lower bounds on the spatial decay of the ground state of the Pauli-Fierz model
Abstract
Lower bounds on the pointwise spatial decay of the ground state of the Pauli-Fierz model in non-relativistic quantum electrodynamics are studied. Two models are considered: the full Pauli-Fierz model and the Pauli-Fierz model under the dipole approximation. For the full model, a lower bound is derived by means of a probabilistic approach based on the Feynman-Kac formula. The application of the Agmon distance method to the full model encounters a serious difficulty arising from the path dependence of a double stochastic integral. In contrast, under the dipole approximation, the corresponding integrand becomes deterministic, which allows a lower bound to be obtained in terms of the Agmon distance.
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BibTeX
@misc{hiroshima2026lower,
title = {{Lower bounds on the spatial decay of the ground state of the Pauli-Fierz model}},
author = {Fumio Hiroshima and Yuki Tsujimoto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.25719},
eprint = {2608.25719},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.25719},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lower bounds on the spatial decay of the ground state of the Pauli-Fierz model
AU - Fumio Hiroshima
AU - Yuki Tsujimoto
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2608.25719
UR - https://arxiv.org/abs/2608.25719
AB - Lower bounds on the pointwise spatial decay of the ground state of the Pauli-Fierz model in non-relativistic quantum electrodynamics are studied. Two models are considered: the full Pauli-Fierz model and the Pauli-Fierz model under the dipole approximation. For the full model, a lower bound is derived by means of a probabilistic approach based on the Feynman-Kac formula. The application of the Agmon distance method to the full model encounters a serious difficulty arising from the path dependence of a double stochastic integral. In contrast, under the dipole approximation, the corresponding integrand becomes deterministic, which allows a lower bound to be obtained in terms of the Agmon distance.
ER -