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On quantum ergodicity for higher dimensional cat maps modulo prime powers
Subham Bhakta, Igor E. Shparlinski
https://arxiv.org/abs/2507.00325 https://

On quantum ergodicity for higher dimensional cat maps modulo prime powers
A discrete model of quantum ergodicity of linear maps generated by symplectic matrices $A \in \mathrm{Sp}(2d,\mathbb{Z})$ modulo an integer $N\ge 1$, has been studied for $d=1$ and almost all $N$ by P. Kurlberg and Z. Rudnick (2001). Their result has been strengthened by J. Bourgain (2005) and subsequently by A. Ostafe, I. E. Shparlinski, and J. F. Voloch (2023). For arbitrary $d$ this has been studied by P. Kurlberg, A. Ostafe, Z. Rudnick and I. E. Shparlinski (2024). The corresponding equidis…

A new type-1 transition in NGC 1346 revealed by (spectro)polarimetry
F. Marin, D. Hutsem\'ekers, S. Jorstad
https://arxiv.org/abs/2507.08589 https://…

A new type-1 transition in NGC 1346 revealed by (spectro)polarimetry
We present the first photo- and spectropolarimetric observations of the changing-look active galactic nucleus NGC~1346 taken with the Perkins telescope (November 2022, March 2025) and VLT/FORS2 (August and September 2024), which have revealed a new spectral transition. We find that NGC~1346 has reverted to its former (2001) type-1 spectral state after having been a type-2 active galactic nucleus from 2004 to 2022. More and more intense broad H$β$ (3720 $\pm$ 310 km.s$^{-1}$ full width at half …