Role of short periodic orbits in quantum maps with continuous openings

Carlos A. Prado, Gabriel G. Carlo, R. M. Benito, and F. Borondo
Phys. Rev. E 97, 042211 – Published 18 April 2018

Abstract

We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity functions. This is relevant in many situations that include optical microresonators and more complicated boundary conditions. In a perturbative regime, the shortest periodic orbits belonging to the classical repeller of the open map—a cantor set given by a region of exactly zero reflectivity—prove to be extremely robust in supporting a set of long-lived resonances of the continuously open quantum maps. Moreover, for steplike functions a significant reduction in the number needed is obtained, similarly to the completely open situation. This happens despite a strong change in the spectral properties when compared to the discontinuous reflectivity case. In order to give a more realistic interpretation of these results we compare with a Fresnel-type reflectivity function.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 8 November 2017
  • Revised 1 March 2018

DOI:https://doi.org/10.1103/PhysRevE.97.042211

©2018 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsAtomic, Molecular & OpticalStatistical Physics & Thermodynamics

Authors & Affiliations

Carlos A. Prado1,2, Gabriel G. Carlo3,*, R. M. Benito4, and F. Borondo5

  • 1Comisión Nacional de Energía Atómica, Departamento de Física, Av. del Libertador 8250, 1429 Buenos Aires, Argentina
  • 2Departamento de Física, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
  • 3Comisión Nacional de Energía Atómica, CONICET, Departamento de Física, Av. del Libertador 8250, 1429 Buenos Aires, Argentina
  • 4Grupo de Sistemas Complejos and Departamento de Física, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, 28040 Madrid, Spain
  • 5Departamento de Química, and Instituto de Ciencias Matemáticas (ICMAT), Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain

  • *carlo@tandar.cnea.gov.ar

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 97, Iss. 4 — April 2018

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×