2013/12/31 by M. A. Bastarrachea-Magnani, Sergio Lerma-Hernández, S. Lerma-Hernandez +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Coupling constant #Excitation #Excited state #Hamiltonian (control theory) #Integrable system #Mathematical physics #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum electrodynamics #Quantum mechanics #Semiclassical physics #Spectroscopy and Quantum Chemical Studies #cond-mat.quant-gas #quant-ph
paper · pdf · doi:10.1103/physreva.89.032101
published as Phys. Rev. A 89, 032101 (2014)
openalex publication_date 2014/03/03 · arxiv created 2014/03/21 · arxiv updated 2014/03/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the nonintegrable Dicke model and its integrable approximation, the Tavis-Cummings model, as functions of both the coupling constant and the excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing the density of states in the semiclassical limit and comparing it with numerical results for the quantum case in large Hilbert spaces, taking advantage of efficient methods recently developed. Two different ESQPTs are identified in both models, which are signaled as singularities in the semiclassical density of states; one static ESQPT occurs for any coupling, whereas a dynamic ESQPT is observed only in the superradiant phase. The role of the unstable fixed points of the Hamiltonian semiclassical flux in the occurrence of the ESQPTs is discussed and determined. Numerical evidence is provided that shows that the semiclassical results describe very well the tendency of the quantum energy spectrum for any coupling in both models. Therefore, the semiclassical density of states can be used to study the statistical properties of the fluctuation in the spectra, a study that is presented in a companion paper.