Semiclassical construction of resonances with hyperbolic structure: the scar function

The formalism of resonances in quantum chaos is improved by using conveniently defined creation-annihilation operators.With these operators at hand, we are able to construct transverse excited resonances at a given Bohrquantized energy.Then, by requiring minimum energy dispersion we obtain solutions in terms of even or odd transverse excitations.These wavefunctions, which are constructed in the vicinity of a periodic orbit with maximum energy localization, provide a precise definition of a scar function.These scar functions acquire, in the semiclassical limit, the hyperbolic structure characteristic of unstable periodic orbits.