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

JA Kuipers, MMA Sieber

Research output: Contribution to journalArticle (Academic Journal)peer-review

17 Citations (Scopus)

Abstract

The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system. We show how these two pictures are related on the semiclassical level. We start from the semiclassical formula with the scattering trajectories and derive from it all terms in the periodic orbit formula for the time delay. The main ingredient in this calculation are correlations between scattering trajectories which are due to trajectories that approach the trapped periodic orbits closely. The equivalence between the two pictures is also demonstrated by considering correlation functions of the time delay. A corresponding calculation for the conductance gives no periodic orbit contributions in leading order.
Translated title of the contributionSemiclassical relation between open trajectories and periodic orbits for the Wigner time delay
Original languageEnglish
Article number046219
Number of pages13
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Volume77
Issue number4
DOIs
Publication statusPublished - 25 Apr 2008

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