2012/07/31 by B. M. Rodríguez-Lara, B M Rodríguez-Lara, H. M. Moya-Cessa +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exact solutions in general relativity #Field (mathematics) #Hamiltonian (control theory) #Orthogonal polynomials #Population #Quantum many-body systems #Random Matrices and Applications #Tridiagonal matrix #Unitary state #Unitary transformation #quant-ph
paper · pdf · doi:10.1088/1751-8113/46/9/095301
published as J. Phys. A: Math. Theor. 46, 095301 (2013) · 12 pages, 3 figures
arxiv created 2013/01/30 · openalex publication_date 2013/02/12 · arxiv updated 2013/02/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show a right unitary transformation approach based on Susskind–Glogower operators that diagonalizes a generalized Dicke Hamiltonian in the field basis and delivers a tridiagonal Hamiltonian in the Dicke basis. This tridiagonal Hamiltonian is diagonalized by a set of orthogonal polynomials satisfying a three-term recurrence relation. Our result is used to deliver a closed form, analytic time evolution for the case of a Jaynes–Cummings–Kerr model and to study the time evolution of the population inversion, reduced field entropy and Husimi's Q -function of the field for ensembles of interacting two-level systems under a Dicke–Kerr model.