Stability and absence of binding for multi-polaron systems

Rupert L. Frank, Elliott H. Lieb, Robert Seiringer, Lawrence E. Thomas

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N≥2 polarons. Fröhlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling √α, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U<2α, stability of matter does hold for U>2α, that is, the ground state energy per particle has a finite limit as N→∞. (ii) There is no binding of any kind if U exceeds a critical value that depends on α but not on N. The same results are shown to hold for the Pekar-Tomasevich model.

Original languageEnglish (US)
Pages (from-to)39-67
Number of pages29
JournalPublications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Issue number1
StatePublished - Jun 2011

All Science Journal Classification (ASJC) codes

  • General Mathematics


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