Pauli-Fierz模型基态空间衰减的下界
Lower bounds on the spatial decay of the ground state of the Pauli-Fierz model
- Kyushu University（九州大学）
- Joint Graduate School of Mathematics for Inovation, Kyushu University（九州大学数学创新联合研究生院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对非相对论量子电动力学的完整Pauli-Fierz模型，用概率方法推导其基态空间衰减下界，因路径依赖问题无法用Agmon距离，而偶极近似下被积函数确定，可通过Agmon距离得到对应下界。
AI中文摘要：
本文研究非相对论量子电动力学中Pauli-Fierz模型基态的逐点空间衰减下界，考虑两类模型：完整Pauli-Fierz模型和偶极近似下的Pauli-Fierz模型。针对完整模型，采用基于Feynman-Kac公式的概率方法推导下界；将Agmon距离方法应用于完整模型时，因双随机积分的路径依赖性遇到严重困难。相比之下，偶极近似下对应被积函数变为确定性，可通过Agmon距离得到下界。
英文摘要：
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.
