Equilibrium Statistical Mechanics of Matter Interacting with the Quantized Radiation Field

  • Klaus Hepp
  • Elliott H. Lieb


The thermodynamic properties of several systems of multilevel atoms interacting with a quantized radiation field are investigated. We allow a quantum-mechanical treatment of the translational degrees of freedom and do not require the rotating-wave approximation. In the finite-photon-mode case one can calculate the free energy per atom in the thermodynamic limit exactly and rigorously. In the infinite-mode case we only get upper and lower bounds, but these are sufficient to give conditions for thermodynamic stability and instability. The kind of phase transition previously found by us for the one-mode Dicke model with the rotating-wave approximation persists in the general multimode case.


Partition Function Coherent State Thermodynamic Limit Photon Mode Translational Degree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Klaus Hepp
    • 1
  • Elliott H. Lieb
    • 2
  1. 1.Department of PhysicsEidgenössische Technische HochschuleZürichSwitzerland
  2. 2.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance

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