| Filter-Diagonalization (M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011(1995)) is a new method for extracting frequencies and damping constants from a short time segment of any time-dependent signal, whether of quantum nature or not. The method is efficient and capable of handling signals with up to millions of (possibly overlapping) frequencies, because it concentrates on specific spectral ranges. Here, we extend the method in several directions. In Chapter 2, we show how the method can be used with a filter of any form. In Chapter 3, we exemplify the performance of the various filters for four different types of signals. The four different types of signals include a correlation signal from a molecular dynamics simulation; a signal from a semiclassical wavepacket propagation (due to Grossmann); a signal from a quantum reactive scattering calculation and two experimental 1-D NMR signals (both ;Heller's expression for the absorption cross-section in the weak field limit is extended to cases where the total Hamiltonian contains a strong time-dependent component, supplemented by a weak field. A very similar expression to the original case then results when the (t,t') formalism is used (Chapter 7); one only needs to construct a correlation function for the system without the weak field, and use it to extract the absorption probability for any value of the weak-field frequency (or pulse shape). In Chapter 8, a numerical approach for extracting Floquet states without full-matrix diagonalization is demonstrated, by filtering (or filter-diagonalization) a single wavefunction (or the correlation function) propagated under the (t,t') Hamiltonian. |
