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The Fröhlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy

Morris Brooks, Robert Seiringer

Abstract

We study the Fröhlich polaron model in $\mathbb{R}^3$, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation.

The Fröhlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy

Abstract

We study the Fröhlich polaron model in , and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation.
Paper Structure (9 sections, 36 theorems, 216 equations)

This paper contains 9 sections, 36 theorems, 216 equations.

Table of Contents

  1. Introduction and Main Results
  2. Models with Cut-off
  3. Construction of a Condensate
  4. Large Deviation Estimates for Strong Condensates
  5. Properties of the Pekar Functional
  6. Proof of Theorem \ref{['Theorem: Main']}
  7. Approximation by Coherent States
  8. Properties of the Pekar Minimizer
  9. Properties of the Projection $\Pi$

Key Result

Theorem 1.1

Let $E_\alpha$ be the ground state energy of $\mathbb{H}$ in Equation-Hamiltonian. For any $s<\frac{1}{29}$ for all $\alpha\geq \alpha(s)$, where $\alpha(s)>0$ is a suitable constant.

Theorems & Definitions (76)

  • Theorem 1.1
  • Definition 2.1
  • Lemma 2.2
  • proof
  • Definition 2.3
  • Lemma 2.4
  • proof
  • Theorem 2.5
  • proof
  • Definition 3.1
  • ...and 66 more