2003/01/15 by Clive Emary, Tobias Brandes · 2 citations
Physics and Astronomy · #cond-mat
paper · pdf · doi:10.1103/physreve.67.066203
published as Phys.Rev.E67:066203,2003 · 51 pages, 15 figures, latex
arxiv created 2003/01/15 · arxiv updated 2009/11/30
We investigate the quantum chaotic properties of the Dicke Hamiltonian; a quantum-optical model which describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. This model exhibits a zero-temperature quantum phase transition in the N \go ∞ limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite N and, by analysing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase-transition. Our considerations of the wavefunction indicate that this is connected with a delocalisation of the system and the emergence of macroscopic coherence. We also derive a semi-classical Dicke model, which exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.