Institut de Physique Théorique
Direction de la Recherche Fondamentale  -  Saclay
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Publication : t17/140

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Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach

Monthus C. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Abstract:
The delocalized non-ergodic phase existing in some random $N times N$ matrix models is analyzed via the Wigner-Weisskopf approximation for the dynamics from an initial site $j_0$. The main output of this approach is the inverse $Gamma_{j_0}(N)$ of the characteristic time to leave the state $j_0$ that provides some broadening $Gamma_{j_0}(N) $ for the weights of the eigenvectors. In this framework, the localized phase corresponds to the region where the broadening $Gamma_{j_0}(N) $ is smaller in scaling than the level spacing $Delta_{j_0}(N) propto frac{1}{N}$, while the delocalized non-ergodic phase corresponds to the region where the broadening $Gamma_{j_0}(N) $ decays with $N$ but is bigger in scaling than the level spacing $Delta_{j_0}(N) $. Then the number $frac{Gamma_{j_0}(N)}{Delta_{j_0}(N)} $ of resonances grows only sub-extensively in $N$. This approach allows to recover the multifractal spectrum of the Generalized-Rosenzweig-Potter (GRP) Matrix model [V.E. Kravtsov, I.M. Khaymovich, E. Cuevas and M. Amini, New. J. Phys. 17, 122002 (2015)]. We then consider the L'evy generalization of the GRP Matrix model, where the off-diagonal matrix elements are drawn with an heavy-tailed distribution of L'evy index $1 Année de publication : 2017
Revue : J. Phys. A 50 295101 (2017)
DOI : 10.1088/1751-8121/aa77e1
Preprint : arXiv:1609.01121
Langue : Anglais

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