Archive ouverte HAL – Multifractality of open quantum systems

Agustín M. Bilen 1 Ignacio García-Mata 1 Bertrand Georgeot 2 Olivier Giraud 3

Agustín M. Bilen, Ignacio García-Mata, Bertrand Georgeot, Olivier Giraud. Multifractality of open quantum systems. Physical Review E , American Physical Society (APS), 2019, 100, pp.032223. ⟨10.1103/PhysRevE.100.032223⟩. ⟨hal-02156304⟩

We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify the relationship between the eigenstates and the classical structures, and we quantify their multifractality at different scales. Based on this study, we conjecture that quantum states in such systems are distributed according to a hierarchy of classical structures, but these states are multifractal instead of ergodic at each level of the hierarchy. This is visible for sufficiently long-lived resonance states at scales smaller than the classical structures. Our results can guide experimentalists in order to observe multifractal behavior in open systems.

  • 1. IFIMAR - Instituto de Investigaciones Físicas de Mar del Plata
  • 2. Information et Chaos Quantiques (LPT)
  • 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques