Proof of the Landau-Pekar Formula for the effective Mass of the Polaron at strong coupling

2024/09/13 by Brooks, Morris
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2409.08835

Abstract

We study the Fröhlich polaron in the regime of strong coupling and prove the asymptotically sharp lower bound on the effective mass m_eff(α)≥ α⁴ m_LP-Cα^4-ε, where m_LP is an explicit constant. Together with the corresponding upper bound, which has been verified recently in [5], we confirm the validity of the celebrated Landau-Pekar formula [12] from 1948 for the effective mass \undersetα→ ∞limα^-4m_eff(α)=m_LP as conjectured by Spohn [25] in 1987.

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