Perturbation series for Jacobi matrices and the quantum Rabi model

Two modified Jacobi methods for M-matrices

Eigenproblem for Jacobi matrices: hypergeometric series solution.

We study the perturbative power series expansions of the eigenvalues and eigenvectors of a general tridiagonal (Jacobi) matrix of dimension d. The (small) expansion parameters are the entries of the two diagonals of length d-1 sandwiching the principal diagonal that gives the unperturbed spectrum. The solution is found explicitly in terms of multivariable (Horn-type) hypergeometric series in 3d...

Dynamical correlation functions and the quantum Rabi model

F. A. Wolf,1 F. Vallone,2 G. Romero,2 M. Kollar,3 E. Solano,2,4 and D. Braak1 1Experimental Physics VI, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany 2Departamento de Quı́mica Fı́sica, Universidad del Paı́s Vasco UPV/EHU, Apartado 644, 48080 Bilbao, Spain 3Theoretical Physics III, Center for Electronic Correlations and Magnetism, University of Au...

Fast Quantum Rabi Model with Trapped Ions

We show how to produce a fast quantum Rabi model with trapped ions. Its importance resides not only in the acceleration of the phenomena that may be achieved with these systems, from quantum gates to the generation of nonclassical states of the vibrational motion of the ion, but also in reducing unwanted effects such as the decay of coherences that may appear in such systems.

two modified jacobi methods for m-matrices