Semiclassical theory of weighted spectra for regular systems: Absorption spectra and decay rates - art. no. 043401

We derive a simple semiclassical representation to describe the large-scale structure of the spectrum of regular systems weighted by some arbitrary fu nction W. Examples of weighted spectra are the width-weighted spectrum, whi ch represents the decay rate of an unstable system, and the oscillator-stre ngth-weighted spectrum, which represents the photoabsorption rate. Semiclas sical representations of such spectra involve stationary-phase contribution s, which are periodic or closed orbits, and end-point contributions, which are loops on an extremal torus. The theory provides the link between semiqu antal formulas and the closed-orbit theory of atomic photoabsorption. It al so allows calculation of an average decay rate without knowledge of the wid ths of individual quantum states.