Communications in Mathematical Physics

, Volume 114, Issue 4, pp 537–548 | Cite as

The equilibrium states of the spin-boson model

  • M. Fannes
  • B. Nachtergaele
  • A. Verbeure


The temperature states of the spin-boson model consisting of a two-level atom in a Bose field are studied. It is proved that for all temperatures there exists a unique solution, hence there is no spontaneous reflection symmetry breaking.


Reflection Neural Network Statistical Physic Equilibrium State Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Leggett, A. J., Chakravarty, S., Dorsey, A. T., Fisher, M. P. A., Garg, Anupam, Zwerger, W.: Dynamics of the dissipative two-state system. Rev. Mod. Phys. 180Google Scholar
  2. 2.
    Davies, E. B.: Symmetry breaking for molecular open systems. Ann. Inst. H. PoincaréA35, 149 (1981)Google Scholar
  3. 3.
    Pfeifer, P.: Chiral Molecules. Diss. ETH N. 6551, Zürich, 1980Google Scholar
  4. 4.
    Spohn, H., Dümcke, R.: Quantum Tunnfling with dissipation and the Ising model over ℝ. J. Stat. Phys.41, 389 (1985)Google Scholar
  5. 5.
    Rocca, F., Sirugue, M., Testard, D.: On a class of equilibrium states under the Kubo-Martin-Schwinger Condition, II. Bosons. Commun. Math. Phys.19, 119 (1970)Google Scholar
  6. 6.
    Bratteli, O., Robinson, D. W.: Operator algebras and quantum statistical mechanics, II. Berlin, Heidelberg, New York: Springer 1981Google Scholar
  7. 7.
    Araki, H., Woods, E. J.: Representations of the canonical commutation relations describing a nonrelativistic infinite free Base gas. J. Math. Phys.4, 637 (1963)Google Scholar
  8. 8.
    Manuceau, J.: Etude de quelques automorphismes de laC*-algebra du champ de bosons libres. Ann. Inst. H. PoincaréVIIIA2, 117 (1968)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • M. Fannes
    • 1
  • B. Nachtergaele
    • 1
  • A. Verbeure
    • 1
  1. 1.Instituut voor Theoretische FysicaUniversiteit LeuvenLeuvenBelgium

Personalised recommendations