The two scenarios for quantum multifractality breakdown

Rémy Dubertrand 1 Ignacio García-Mata 2 Bertrand Georgeot 1 Olivier Giraud 3 Gabriel Lemarié 1 J. Martin 4

Physical Review Letters, American Physical Society, 2014, 112, pp.234101. <10.1103/PhysRevLett.112.234101>

We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Our results suggest that quantum multifractality breakdown is universal and follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications.

  • 1. Information et Chaos Quantiques (LPT)
  • 2. Instituto de Investigaciones Físicas de Mar del Plata
  • 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 4. Institut de Physique Nucléaire, Atomique et de Spectroscopie