Multifractality of quantum wave packets

Ignacio Garcia-Mata (1, 2, 3) , J. Martin (4) , Olivier Giraud (5) , Bertrand Georgeot (2)

1 IFIMAR - Instituto de Investigaciones Físicas de Mar del Plata
2 ICQ - Cohérence Quantique (LPT)
3 LPT - Laboratoire de Physique Théorique
4 Institut de Physique Nucl'eaire, Atomique et de Spectroscopie
5 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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.

Domaines: Dynamique Chaotique [nlin.CD]; Autre [cond-mat.other]

Ignacio Garcia-Mata, J. Martin, Olivier Giraud, Bertrand Georgeot. Multifractality of quantum wave packets. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2012, 86, pp.056215. ⟨10.1103/PhysRevE.86.056215⟩. ⟨hal-00715829⟩