Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe

DY: Dynamik und Statistische Physik

DY 52: Quantum chaos II

DY 52.4: Vortrag

Freitag, 28. März 2003, 12:15–12:30, G\"OR/226

Perturbations of low rank: Applications to quantum billiards — •Thomas Gorin¹ and Jan Wiersig² — ¹Theoretische Quantendynamik, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, D-79104 Freiburg — ²Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden

We present a method to calculate eigenvalues and eigenvectors of a Hamiltonian which consists of a diagonal part, and a positive perturbation of rank M. The power of the method lies in the fact that one has to diagonalize a matrix K(E), which is only of dimension M. If the matrix K(E) fulfills a certain secular equation, only then is E an eigenvalue of the Hamiltonian. The positivity of the perturbation allows to calculate the number of eigenvalues in a given interval, by only two diagonalisations of K(E) at the interval boundaries.

We then use this method to calculate long level sequences at high level numbers for different twodimensional quantum billiards.