Biomedical subjects

G Wunner

Publications and source records attributed to G Wunner.

15 recordsLinked to original sources

PubMed2001

Semiclassical quantization by harmonic inversion: comparison of algorithms.

Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been proposed for this purpose. Our aim is to find out which method is numerically most efficient. To this end, we summarize and discuss the different techniques and compare their accuracies by way of two example systems.

Journal Article↗

PubMed1999

Semiclassical non-trace-type formulas for matrix-element fluctuations and weighted densities of states.

Densities of states weighted with the diagonal matrix elements of two operators A and B, i.e., rho(A,B)(E)= summation operator(n) delta(E-E(n)), cannot, in general, be written as a trace formula, and therefore no simple extension of semiclassical trace formulas is known for this case. However, from the high resolution analysis of quantum spectra in the semiclassical regime we find strong evidence that weighting the delta functions in the quantum mechanical density of states with the product of diagonal matrix elements, , is equivalent to weighting the periodic orbit contributions in the semiclassical periodic orbit sum with the product of the periodic orbit means, (p) (p), of the classical observables A and B. Results are presented for the hydrogen atom in a magnetic field for both the chaotic and near-integrable regime, and for the circle billiard.

Journal Article↗

PubMed1999

Semiclassical spectra and diagonal matrix elements by harmonic inversion of cross-correlated periodic orbit sums.

Semiclassical spectra weighted with products of diagonal matrix elements of operators A(alpha), i.e., g(alphaalpha')(E)= summation operator(n) /(E-E(n)), are obtained by harmonic inversion of a cross-correlation signal constructed of classical periodic orbits. The method provides highly resolved semiclassical spectra even in situations of nearly degenerate states, and opens the way to reducing the required signal lengths to shorter than the Heisenberg time. This implies a significant reduction of the number of orbits required for periodic orbit quantization by harmonic inversion.

Journal Article↗

PubMed1996