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pro vyhledávání: '"Monvel Anne"'
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:
Monvel Anne, Zielinski Lech
Publikováno v:
Open Mathematics, Vol 12, Iss 3, Pp 445-463 (2014)
Externí odkaz:
https://doaj.org/article/f58e7cf9c7a24ffdbef39ac21f2798d6
We consider the focusing integrable nonlocal nonlinear Schr\"odinger equation \[\mathrm{i}q_{t}(x,t)+q_{xx}(x,t)+2q^{2}(x,t)\bar{q}(-x,t)=0\] with asymmetric nonzero boundary conditions: $q(x,t)\to\pm A\mathrm{e}^{-2\mathrm{i}A^2t}$ as $x\to\pm\infty
Externí odkaz:
http://arxiv.org/abs/2202.13327
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