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Effective density of states for a quantum oscillator coupled to a photon field
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Betz, Volker and Castrigiano, Domenico P. L.. (2011) Effective density of states for a quantum oscillator coupled to a photon field. Communications in Mathematical Physics, Volume 301 (Number 3). pp. 811839. ISSN 00103616
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Official URL: http://dx.doi.org/10.1007/s0022001011678
Abstract
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.
Item Type:  Journal Article  

Subjects:  Q Science > QC Physics  
Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Harmonic oscillators, Quantum field theory, Hamiltonian systems  
Journal or Publication Title:  Communications in Mathematical Physics  
Publisher:  Springer  
ISSN:  00103616  
Official Date:  2011  
Dates: 


Volume:  Volume 301  
Number:  Number 3  
Page Range:  pp. 811839  
Identification Number:  10.1007/s0022001011678  
Status:  Peer Reviewed  
Publication Status:  Published  
Funder:  Engineering and Physical Sciences Research Council (EPSRC)  
Grant number:  EP/D07181X/1 (EPSRC)  
References:  1. Bach, V., Fröhlich, J., Sigal, I.M.: Quantum Electrodynamics of Conﬁned Nonrelativistic Particles. Adv. 

URI:  http://wrap.warwick.ac.uk/id/eprint/41674 
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