Delocalization and quantum chaos in atom-field systems

2015/09/19 by M. A. Bastarrachea-Magnani, B. López-del-Carpio, Jorge Chávez-Carlos +5 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Atom (system on chip) #Basis (linear algebra) #CHAOS (operating system) #Chaotic #Computer science #Delocalized electron #Field (mathematics) #Geometry #Lyapunov exponent #Mathematics #Nonlinear system #Phase space #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Space (punctuation) #Square root #Statistical physics #quant-ph

paper · pdf · doi:10.1103/physreve.93.022215

published as Phys. Rev. E 93, 022215 (2016) · 11 Pages, 8 Figures, 1 Table

arxiv created 2015/09/19 · openalex publication_date 2016/02/22 · arxiv updated 2016/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest nonintegrable atom-field system, the Dicke model. A close correlation between the classical Lyapunov exponents and the quantum Participation Ratio of coherent states on the eigenenergy basis is exhibited for different points in the phase space. It is also shown that the Participation Ratio scales linearly with the number of atoms in chaotic regions and with its square root in the regular ones.

Citations

• Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED
• Quantum quenches, thermalization, and many-body localization
• Decoherence due to an excited-state quantum phase transition in a two-level boson model
• Concise analytic solutions to the quantum Rabi model with two arbitrary qubits
• Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation
• Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model
• Quantum many-body systems out of equilibrium
• Electrons in disordered systems and the theory of localization
• Decoherence as a signature of an excited-state quantum phase transition

Cited by

• Experimental realization of the classical Dicke model
• Positive quantum Lyapunov exponents in experimental systems with a regular classical limit