|
Abstract |
Multifractality is an exotic property that emerges at the Anderson transition.
Meanwhile, the dynamics are highly influenced by the multifractality of the
eigenstates. This presentation will focus on the emergence of multifractality
and its dynamic signatures in random-matrix ensembles amenable to analytical
treatment. Firstly, I will revisit random-matrix ensembles that capture
multifractal properties in finite dimensions, emphasizing the scale-invariant
properties of dynamics as a consequence of multifractality. Secondly, I will
introduce new random-matrix ensembles featuring critical properties in infinite
dimension, the upper critical dimension of the Anderson transition. Through
analytical arguments, these models reveal two scenarios of critical properties:
logarithmic multifractality and critical localization. These results will help
to clarify some elusive problems of Anderson transitions in random graphs.
[references: Physical Review E 108(5) , 054127 (2023) & arXiv:2312.17481 (2023)] |
