Multifractality of quantum wave packets

Ignacio Garcia-Mata 12, J. Martin 3, Olivier Giraud 4, Bertrand Georgeot 1

Physical Review E 86 (2012) 056215

We study a version of the mathematical Ruijsenaars-Schneider model, and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets, and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, different from the mulifractality of eigenvectors, but related to it, as is the rate of the decrease. Our results are relevant to experimental situations.

  • 1 : Laboratoire de Physique Théorique - IRSAMC (LPT)
    CNRS : UMR5152 – Université Paul Sabatier (UPS) - Toulouse III
  • 2 : Instituto de Investigaciones F'ısicas de Mar del Plata (IFIMAR)
    Univ. Nacional de La Plata and Conicet
  • 3 : Institut de Physique Nucl'eaire, Atomique et de Spectroscopie
    Université de Liège
  • 4 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
    CNRS : UMR8626 – Université Paris XI - Paris Sud