Year: 2026
Type: article
Abstract: We study the Fröhlich polaron in the regime of strong coupling and prove the asymptotically sharp lower bound on the effective mass $m_{\mathrm{eff}}(\alpha )\geq \alpha ^{4} m_{\mathrm{LP}}-C\alpha ^{4- \epsilon }$ m eff ( α ) ≥ α 4 m LP − C α 4 − ϵ , where $m_{\mathrm{LP}}$ m LP is the constant predicted by L. D. Landau and S. I. Pekar [13] in 1948 for the effective mass of the classical polaron. Together with the corresponding upper bound, recently verified by R. Seiringer and the author, we confirm the validity of the celebrated Landau-Pekar formula for the effective mass of the Fröhlich polaron $\underset{\alpha \rightarrow \infty }{\lim }\alpha ^{-4}m_{ \mathrm{eff}}(\alpha )=m_{\mathrm{LP}}$ lim α → ∞ α − 4 m eff ( α ) = m LP , which has been conjectured by H. Spohn [27] in 1987.
Source: Inventiones mathematicae
Author: Morris Brooks
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4403662161