Zobrazeno 1 - 10
of 70
pro vyhledávání: '"Sabri, Mostafa"'
This paper is devoted to the investigation of the spectral theory and dynamical properties of periodic graphs which are not locally finite but carry non-negative, symmetric and summable edge weights. These graphs are shown to exhibit rather intriguin
Externí odkaz:
http://arxiv.org/abs/2411.14965
Autor:
de Monvel, Anne Boutet, Sabri, Mostafa
We give several quantum dynamical analogs of the classical Kronecker-Weyl theorem, which says that the trajectory of free motion on the torus along almost every direction tends to equidistribute. As a quantum analog, we study the quantum walk $\exp(-
Externí odkaz:
http://arxiv.org/abs/2312.04492
Autor:
Sabri, Mostafa, Youssef, Pierre
We study flat bands of periodic graphs in a Euclidean space. These are infinitely degenerate eigenvalues of the corresponding adjacency matrix, with eigenvectors of compact support. We provide some optimal recipes to generate desired bands, some suff
Externí odkaz:
http://arxiv.org/abs/2304.06465
Autor:
Mckenzie, Theo, Sabri, Mostafa
We prove quantum ergodicity for a family of periodic Schr\"odinger operators $H$ on periodic graphs. This means that most eigenfunctions of $H$ on large finite periodic graphs are equidistributed in some sense, hence delocalized. Our results cover th
Externí odkaz:
http://arxiv.org/abs/2208.12685
Autor:
Ammari, Kaïs, Sabri, Mostafa
In this short note we prove a sharp dispersive estimate $\|\mathrm{e}^{\mathrm{i} tH} f\|_\infty < t^{-d/3}\|f\|_1$ for any Cartesian product $\mathbb{Z}^d\mathop\square G_F$ of the integer lattice and a finite graph. This includes the infinite ladde
Externí odkaz:
http://arxiv.org/abs/2208.10805
Autor:
de Monvel, Anne Boutet, Sabri, Mostafa
We prove ballistic transport of all orders, that is, $\lVert x^m\mathrm{e}^{-\mathrm{i}tH}\psi\rVert\asymp t^m$, for the following models: the adjacency matrix on $\mathbb{Z}^d$, the Laplace operator on $\mathbb{R}^d$, periodic Schr\"odinger operator
Externí odkaz:
http://arxiv.org/abs/2202.00940
We consider a sequence of finite quantum graphs with few loops, so that they converge, in the sense of Benjamini-Schramm, to a random infinite quantum tree. We assume these quantum trees are spectrally delocalized in some interval $I$, in the sense t
Externí odkaz:
http://arxiv.org/abs/2102.04169
Autor:
Ammari, Kaïs, Sabri, Mostafa
We prove dispersive estimates for two models~: the adjacency matrix on a discrete regular tree, and the Schr\"odinger equation on a metric regular tree with the same potential on each edge/vertex. The latter model can be thought of as an extension of
Externí odkaz:
http://arxiv.org/abs/2009.03153
We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graphs, means that the restriction of the quantum graph to a randomly chose
Externí odkaz:
http://arxiv.org/abs/2008.05709
We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum consists
Externí odkaz:
http://arxiv.org/abs/2003.12765