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

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

2010-02-20

arxiv.org/abs/1002.3932v1

Phys. Rev. B 82, 024305 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

14 pages, 4 figures

Scientific paper

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}, where sqrt{} is an effective coupling strength between the two-level systems and the boson.

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