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We show that in the few-excitation regime the classical and quantumtime-evolution of the inhomogeneous Dicke model for N two-level systems coupledto a single boson mode agree for N>>1. In the presence of a single excitationonly, the leading term in an 1/N-expansion of the classical equations of motionreproduces the result of the Schroedinger equation. For a small number ofexcitations, the numerical solutions of the classical and quantum problemsbecome equal for N sufficiently large. By solving the Schroedinger equationexactly for two excitations and a particular inhomogeneity we obtain1/N-corrections which lead to a significant difference between the classicaland quantum solutions at a new time scale which we identify as an Ehrenfersttime, given by tau_E=sqrt{N<g^2>}, where sqrt{<g^2>} is an effective couplingstrength between the two-level systems and the boson.

The classical and quantum dynamics of the inhomogeneous Dicke model and its Ehrenfest time