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Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling

Robert Seiringer

Abstract

We consider a class of polaron models, including the Fröhlich model, at zero total momentum, and show that at sufficiently weak coupling there are no excited eigenvalues below the essential spectrum.

Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling

Abstract

We consider a class of polaron models, including the Fröhlich model, at zero total momentum, and show that at sufficiently weak coupling there are no excited eigenvalues below the essential spectrum.
Paper Structure (3 sections, 3 theorems, 46 equations)

This paper contains 3 sections, 3 theorems, 46 equations.

Table of Contents

  1. Main Result
  2. Proof of Theorem \ref{['thm:main']}
  3. Technical bounds

Key Result

Theorem 1.1

There exists a $g_0 > 0$ such that for $0\leq g < g_0$, $H$ has only one eigenvalue below its essential spectrum. In particular, the spectrum of $H$ equals $\sigma(H) = \{E_0\} \cup [E_0 + 1,\infty)$.

Theorems & Definitions (7)

  • Theorem 1.1
  • Lemma 2.1
  • Remark 2.2
  • proof : Proof of Lemma \ref{['lem:main']}
  • Lemma 2.3
  • proof : Proof of Lemma \ref{['lem:aux']}
  • Remark 2.4