Dresden 2003 – scientific programme
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DY: Dynamik und Statistische Physik
DY 52: Quantum chaos II
DY 52.4: Talk
Friday, March 28, 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.