%0 Journal Article
%T The classical and quantum dynamics of the inhomogeneous Dicke model and its Ehrenfest time
%A Oleksandr Tsyplyatyev
%A Daniel Loss
%J Physics
%D 2010
%I arXiv
%R 10.1103/PhysRevB.82.024305
%X We show that in the few-excitation regime the classical and quantum time-evolution of the inhomogeneous Dicke model for N two-level systems coupled to a single boson mode agree for N>>1. In the presence of a single excitation only, the leading term in an 1/N-expansion of the classical equations of motion reproduces the result of the Schroedinger equation. For a small number of excitations, the numerical solutions of the classical and quantum problems become equal for N sufficiently large. By solving the Schroedinger equation exactly for two excitations and a particular inhomogeneity we obtain 1/N-corrections which lead to a significant difference between the classical and quantum solutions at a new time scale which we identify as an Ehrenferst time, given by tau_E=sqrt{N<g^2>}, where sqrt{<g^2>} is an effective coupling strength between the two-level systems and the boson.
%U http://arxiv.org/abs/1002.3932v1