Mw. Beims et al., Semiclassical theory of weighted spectra for regular systems: Absorption spectra and decay rates - art. no. 043401, PHYS REV A, 6204(4), 2000, pp. 3401
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.