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The Wigner time delay of a classically chaotic quantum system can beexpressed semiclassically either in terms of pairs of scattering trajectoriesthat enter and leave the system or in terms of the periodic orbits trappedinside the system. We show how these two pictures are related on thesemiclassical level. We start from the semiclassical formula with thescattering trajectories and derive from it all terms in the periodic orbitformula for the time delay. The main ingredient in this calculation is a newtype of correlation between scattering trajectories which is due totrajectories that approach the trapped periodic orbits closely. The equivalencebetween the two pictures is also demonstrated by considering correlationfunctions of the time delay. A corresponding calculation for the conductancegives no periodic orbit contributions in leading order.

The semiclassical relation between open trajectories and periodic orbits for the Wigner time delay