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arXiv · 2608.25719

Lower bounds on the spatial decay of the ground state of the Pauli-Fierz model

Fumio Hiroshima·Yuki Tsujimoto
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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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Fumio Hiroshima, Yuki Tsujimoto. 2026-08-26. Lower bounds on the spatial decay of the ground state of the Pauli-Fierz model. https://arxiv.org/abs/2608.25719

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