Communications in Mathematical Physics

, Volume 301, Issue 3, pp 811–839 | Cite as

Effective Density of States for a Quantum Oscillator Coupled to a Photon Field

  • Volker BetzEmail author
  • Domenico P. L. Castrigiano


We give an explicit formula for the effective partition function of a harmonically bound particle minimally coupled to a photon field in the dipole approximation. The effective partition function is shown to be the Laplace transform of a positive Borel measure, the effective measure of states. The absolutely continuous part of the latter allows for an analytic continuation, the singularities of which give rise to resonances. We give the precise location of these singularities, and show that they are well approximated by first order poles with residues equal to the multiplicities of the corresponding eigenspaces of the uncoupled quantum oscillator. Thus we obtain a complete analytic description of the natural line spectrum of the charged oscillator.


Partition Function Analytic Continuation Effective Density Quantum Oscillator Order Pole 
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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WarwickCoventryEngland
  2. 2.Fakultät für MathematikTU MünchenGarchingGermany

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