title: Theory of short periodic orbits for partially open quantum maps.
abstract: We extend the semiclassical theory of short periodic orbits [M. Novaes et al., Phys. Rev. E 80, 035202(R) (2009)PLEEE81539-375510.1103/PhysRevE.80.035202] to partially open quantum maps, which correspond to classical maps where the trajectories are partially bounced back due to a finite reflectivity R. These maps are representative of a class that has many experimental applications. The open scar functions are conveniently redefined, providing a suitable tool for the investigation of this kind of system. Our theory is applied to the paradigmatic partially open tribaker map. We find that the set of periodic orbits that belongs to the classical repeller of the open map (R=0) is able to support the set of long-lived resonances of the partially open quantum map in a perturbative regime. By including the most relevant trajectories outside of this set, the validity of the approximation is extended to a broad range of R values. Finally, we identify the details of the transition from qualitatively open to qualitatively closed behavior, providing an explanation in terms of short periodic orbits.
authors: Departamento de Física, Comisión Nacional de Energía Atómica, CONICET, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina.
authors: Gabriel G
authors: GG
authors: Carlo
authors: Grupo de Sistemas Complejos and Departamento de Física, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, 28040 Madrid, Spain.
authors: R M
authors: RM
authors: Benito
authors: Departamento de Química and Instituto de Ciencias Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain.
authors: F
authors: F
authors: Borondo