condition. [4/4 of https://arxiv.org/abs/2502.11445v1]

positive mass on $\Lambda_{\omega}$. The premise is that we can obatain a family of quasimodes for the $h-$differential operator $P_{h}(t)$ in the semiclassical limit as $h\rightarrow0$, under the $\sigma$-Bruno-R\"{u}ssmann [3/4 of https://arxiv.org/abs/2502.11445v1]

$\sigma$-Bruno-R\"{u}ssmann condition, instead of the Diophantine one. Its equivalence is described as: for almost all perturbed Hamiltonian's KAM Lagrangian tori $\Lambda_{\omega}$, there exists a semiclassical measure with [2/4 of https://arxiv.org/abs/2502.11445v1]

arXiv:2502.11445v1 Announce Type: new
Abstract: We show that the eigenfunctions of the self-adjoint elliptic $h-$differential operator $P_{h}(t)$ exhibits semiclassical scar phenomena on the $d-$dimensional torus, under the [1/4 of https://arxiv.org/abs/2502.11445v1]

as an one-time pad. The main advantages are strict aperiodicity of such sets and rather short key that uniquely defines quasicrystal. [2/2 of https://arxiv.org/abs/2502.10468v1]

arXiv:2502.10468v1 Announce Type: new
Abstract: We propose a modification of the classical Vernam cipher based on properties of one-dimensional quasicrystals. The method uses the sequence of quasicrystal minimal distances [1/2 of https://arxiv.org/abs/2502.10468v1]