Properties of the energy–momentum relation for the Fröhlich polaron are of continuing interest, especially for large values of the coupling constant. By combining spectral theory with the available results on the central limit theorem for the polaron path measure, we prove that, except for an intermediate range of couplings, the inverse effective mass is strictly positive and coincides with the diffusion constant. Such a result is established also for polaron-type models with a suitable ultraviolet cut-off and for arbitrary values of the coupling constant. We point out a slightly stronger variant of the central limit theorem which would imply that the energy–momentum relation has a unique global minimum attained at zero momentum.

中文翻译：

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极化子的有效质量-修订

Fröhlich极化子的能量-动量关系的性质一直受到关注，特别是对于较大的耦合常数。通过将光谱理论与极化子路径测度的中心极限定理的现有结果相结合，我们证明，除了中间范围的耦合以外，逆有效质量严格为正，并且与扩散常数一致。对于具有合适的紫外线截止值的极化子型模型以及耦合常数的任意值，也可以建立这样的结果。我们指出了中心极限定理的一个稍强的变体，这暗示着能量动量关系在零动量下具有唯一的全局最小值。