Canonical form of Hamiltonian matrices

The Canonical Form of the Rabi Hamiltonian

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the BargmannFock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional e...

Spectral statistics of Hamiltonian matrices in tridiagonal form

R. A. Molina,1,2 A. P. Zuker,3 A. Relaño,4 and J. Retamosa4 1Commissariat a l’Energie Atomique, Service de Physique de l’Etat Condensé, F-91191 Gif-sur-Yvette, France 2Max-Planck-institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany 3IReS, Bât27, IN2P3-Centre National de la Recherche Scientifique/Université Louis Pasteur BP 28, F-67037 Strasbourg Cedex 2, France...

Crossing Matrices and Thurston's Canonical Form for Braids

Properties of Central Symmetric X-Form Matrices

In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

Hamiltonian Square Roots of Skew-Hamiltonian Matrices

We present a constructive existence proof that every real skew-Hamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasi-Jordan canonical form via symplectic similarity. We show further that every W has infinitely many real Hamiltonian square roots, and give a lower bound on the dimension of the set of all suc...