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pro vyhledávání: '"Sadel, Christian"'
In this paper, we develop the radial transfer matrix formalism for unitary one-channel operators. This generalizes previous formalisms for CMV matrices and scattering zippers. We establish an analog of Carmona's formula and deduce criteria for absolu
Externí odkaz:
http://arxiv.org/abs/2405.08898
For a generalized Su-Schrieffer-Heeger model the energy zero is always critical and hyperbolic in the sense that all reduced transfer matrices commute and have their spectrum off the unit circle. Disorder driven topological phase transitions in this
Externí odkaz:
http://arxiv.org/abs/2303.09816
Autor:
Gonzales, Hernan, Sadel, Christian
We consider a family of random Schr\"odinger operators on the discrete strip with decaying random $\ell^2$ matrix potential. We prove that the spectrum is almost surely pure absolutely continuous, apart from random, possibly embedded eigenvalues, whi
Externí odkaz:
http://arxiv.org/abs/2202.02936
Autor:
Sadel, Christian
We introduce a transfer matrix method for the spectral analysis of discrete Hermitian operators with locally finite hopping. Such operators can be associated with a locally finite graph structure and the method works in principle on any such graph. T
Externí odkaz:
http://arxiv.org/abs/1903.10114
Autor:
Sadel, Christian
Sequences of certain finite graphs, antitrees, are constructed along which the Anderson model shows GOE statistics, i.e. a re-scaled eigenvalue process converges to the ${\rm Sine}_1$ process. The Anderson model on the graph is a random matrix being
Externí odkaz:
http://arxiv.org/abs/1710.05253
A Floquet systems is a periodically driven quantum system. It can be described by a Floquet operator. If this unitary operator has a gap in the spectrum, then one can define associated topological bulk invariants which can either only depend on the b
Externí odkaz:
http://arxiv.org/abs/1708.01173
Autor:
Sadel, Christian
Publikováno v:
Journal of Functional Analysis, 274 (2018), 2205-2244
A one-channel operator is a self-adjoint operator on $\ell^2(\mathbb{G})$ for some countable set $\mathbb{G}$ with a rank 1 transition structure along the sets of a quasi-spherical partition of $\mathbb{G}$. Jacobi operators are a very special case.
Externí odkaz:
http://arxiv.org/abs/1703.08055
Autor:
Sadel, Christian
Publikováno v:
In Journal of Functional Analysis 15 October 2021 281(8)
Autor:
Sadel, Christian, Xu, Disheng
We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form. As a cons
Externí odkaz:
http://arxiv.org/abs/1601.06118
Autor:
Sadel, Christian
We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional structure al
Externí odkaz:
http://arxiv.org/abs/1501.04287