Zobrazeno 1 - 10
of 98
pro vyhledávání: '"Band, Ram"'
We present a review of the work L. Raymond from 1995. The review aims at making this work more accessible and offers adaptations of some statements and proofs. In addition, this review forms an applicable framework for the complete solution of the Dr
Externí odkaz:
http://arxiv.org/abs/2409.10920
We study periodic approximations of aperiodic Schr\"odinger operators on lattices in Lie groups with dilation structure. The potentials arise through symbolic substitution systems that have been recently introduced in this setting. We characterize co
Externí odkaz:
http://arxiv.org/abs/2408.09282
The Dry Ten Martini Problem for Sturmian Hamiltonians is affirmatively solved. Concretely, we prove that all spectral gaps are open for Schr\"odinger operators with Sturmian potentials and non-vanishing coupling constant. A key approach towards the s
Externí odkaz:
http://arxiv.org/abs/2402.16703
Autor:
Band, Ram, Charron, Philippe
We prove upper and lower bounds for the number of zeroes of linear combinations of Schr\"odinger eigenfunctions on metric (quantum) graphs. These bounds are distinct from both the interval and manifolds. We complement these bounds by giving non-trivi
Externí odkaz:
http://arxiv.org/abs/2310.03877
This extended Oberwolfach report (to appear in the proceedings of the MFO Workshop 2335: Aspects of Aperiodic Order) announces the full solution to the Dry Ten Martini Problem for Sturmian Hamiltonians. Specifically, we show that all spectral gaps of
Externí odkaz:
http://arxiv.org/abs/2309.04351
We consider the Laplacian on a metric graph, equipped with Robin ($\delta$-type) vertex condition at some of the graph vertices and Neumann-Kirchhoff condition at all others. The corresponding eigenvalues are called Robin eigenvalues, whereas they ar
Externí odkaz:
http://arxiv.org/abs/2212.12531
An eigenfunction of the Laplacian on a metric (quantum) graph has an excess number of zeros due to the graph's non-trivial topology. This number, called the nodal surplus, is an integer between 0 and the graph's first Betti number $\beta$. We study t
Externí odkaz:
http://arxiv.org/abs/2106.06096
Publikováno v:
Analysis & PDE 16 (2023) 2147-2171
A Laplacian eigenfunction on a two-dimensional Riemannian manifold provides a natural partition into Neumann domains (a.k.a. a Morse--Smale complex). This partition is generated by gradient flow lines of the eigenfunction, which bound the so-called N
Externí odkaz:
http://arxiv.org/abs/2009.14564
Autor:
Alon, Lior, Band, Ram
Publikováno v:
Annales Henri Poincar\'e, 2021, (), 1-64
The Neumann points of an eigenfunction $f$ on a quantum (metric) graph are the interior zeros of $f'$. The Neumann domains of $f$ are the sub-graphs bounded by the Neumann points. Neumann points and Neumann domains are the counterparts of the well-st
Externí odkaz:
http://arxiv.org/abs/1911.12435
Publikováno v:
Symmetry 2019, 11(2), 185
We consider stationary waves on nonlinear quantum star graphs, i.e. solutions to the stationary (cubic) nonlinear Schr\"odinger equation on a metric star graph with Kirchhoff matching conditions at the centre. We prove the existence of solutions that
Externí odkaz:
http://arxiv.org/abs/1901.04275