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Peer-reviewedCC BYInventiones mathematicae

Proof of the Landau-Pekar formula for the effective mass of the polaron at strong coupling

  • Morris Brooks1
  1. 1Zürich, Switzerland
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Abstract

We study the Fröhlich polaron in the regime of strong coupling and prove the asymptotically sharp lower bound on the effective mass meff(α )≥ α 4 mLP−Cα 4− ϵ m eff ( α ) ≥ α 4 m LP − C α 4 − ϵ , where mLP 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 undersetα → ∞ lim α −4m eff(α )=mLP lim α → ∞ α − 4 m eff ( α ) = m LP , which has been conjectured by H. Spohn [27] in 1987.

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Cite

BibTeXRIS
BibTeX
@article{brooks2026proof,
  title = {{Proof of the Landau-Pekar formula for the effective mass of the polaron at strong coupling}},
  author = {Morris Brooks},
  journal = {Inventiones mathematicae},
  year = {2026},
  month = jul,
  doi = {10.1007/s00222-026-01440-6},
  url = {https://doi.org/10.1007/s00222-026-01440-6},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Proof of the Landau-Pekar formula for the effective mass of the polaron at strong coupling
AU  - Morris Brooks
PY  - 2026
DA  - 2026/07/28
JO  - Inventiones mathematicae
DO  - 10.1007/s00222-026-01440-6
UR  - https://doi.org/10.1007/s00222-026-01440-6
AB  - 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 )≥ α ^4 m_LP−Cα ^4− ϵ  m eff ( α ) ≥ α 4 m LP − C α 4 − ϵ , where m_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 undersetα → ∞ lim α ^−4m_ eff(α )=m_LP lim α → ∞ α − 4 m eff ( α ) = m LP , which has been conjectured by H. Spohn [27] in 1987.
SN  - 0020-9910
SN  - 1432-1297
ER  -