Wednesday, February 15, 2023 - 09:00 in ZOOM - Video Conference
Non-ergodic extended states in the beta-ensemble
A talk in the Seminar Zufallsmatrizen series by
Adway Kumar Das from Indian Institute of Science Education and Research Kolkata
| Abstract: |
The $\beta$-ensemble involves a joint density of energy levels where $\beta$ can be
understood as the inverse temperature of an equivalent Coulomb gas model.
Dumitriu and Edelman proposed a matrix representation of $\beta$-ensemble. If we
consider $\beta=N^{−\gamma}$ then we find that the Anderson localization-delocalization
transition occurs at $\gamma=1$ and ergodicity breaks down at $\gamma=0$. Thus Non-Ergodic
Extended (NEE) phase is observed over a finite interval of parameter values (
$0<\gamma<1$). We find that the level repulsion-clustering transition coincides with the
breaking of ergodicity while long-range correlation among the energy levels
exhibit a heterogeneous behavior in the NEE regime. We also observe that there
are $O(N^{\gamma})$ localized states in the NEE regime which indicates a possibility of
spectral inhomogeneity.
Based on the work under the supervision of Anandamohan Ghosh
(10.1103/PhysRevE.105.054121).
Please contact Leslie Molag
(lmolag@math.uni-bielefeld.de) for details regarding access.
Within the CRC this talk is associated to the project(s): C6 |
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