The Driven Dicke Models

  • S. S. Hassan
  • G. P. Hildred
  • R. R. Puri
  • R. K. Bullough
Conference paper


Master equations are being used increasingly in quantum optics.1 The method consists of deriving an equation for the evolution of the reduced density operator ρa for the subsystem A of the composite system R+A: R is a reservoir whose correlations are assumed to decay faster than the transients of A. One starts from the Liouville equation for the system density operator ρr+a and by defining a suitable projection operator P one obtains an integro differential equation for Pρr+a. Usually P =ρR(O)Tr where pR(O) is the initial density operator of R and the final working equation for p is usually found in Born and Markov approximations. But it has been argued2 that this definition of P together with Born and Markov approximations introduces a decoupling between R and A. To avoid this one may take recourse to time dependent projection operators2 which therefore introduce additional complications. We shall use this note, which also surveys our recent work on the driven Dicke model, to point out the limitations of the usual projection operator method.


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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • S. S. Hassan
    • 2
  • G. P. Hildred
    • 1
  • R. R. Puri
    • 1
  • R. K. Bullough
    • 1
  1. 1.Department of MathematicsUMISTManchesterUK
  2. 2.Ain Shams UniversityCairoEgypt

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