Remarks on the ground state energy of the spin-boson model. An application of the Wigner-Weisskopf model

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Abstract

For the ground state energy of the spin-boson (SB) model, we give a new upper bound in the case with infrared singularity condition (i.e. without infrared cutoff), and a new lower bound in the case of massless bosons with infrared regularity condition. We first investigate spectral properties of the Wigner-Weisskopf (WW) model, and apply them to SB model to achieve our purpose. Then, as an extra result of the spectral analysis for WW model, we show that a non-perturbative ground state appears, and its ground state energy is so low that we cannot conjecture it by using the regular perturbation theory.

Original languageEnglish
Pages (from-to)221-251
Number of pages31
JournalReviews in Mathematical Physics
Volume13
Issue number2
DOIs
Publication statusPublished - Feb 1 2001
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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