On the Essential Spectrum of Quantum Graphs
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DOI: 10.1007/s00020-017-2386-6
Abstract: Let $$\Gamma \subset \mathbb {R}^{n}$$Γ⊂Rn be a graph periodic with respect to the action of a group $$\mathbb {G}$$G isomorphic to $$\mathbb {Z}^{m},1\le m\le n. $$Zm,1≤m≤n. We consider a one-dimensional Schrödinger operator $$\begin{aligned} S_{q}u(x)=\left( -\frac{d^{2}}{dx^{2}}+q(x)\right)… read more here.
Keywords: quantum graphs; spectrum; essential spectrum; spectrum quantum ... See more keywords
On the Weyl Law for Quantum Graphs
Sign Up to like & getrecommendations! Published in 2019 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-017-0469-9
Abstract: Roughly speaking, the Weyl law describes the asymptotic distribution of eigenvalues of the Laplacian that can be attached to different objects and can be analyzed in different settings. The form of the remainder term in… read more here.
Keywords: form; law; term; quantum graphs ... See more keywords
Narrow peaks of full transmission in simple quantum graphs
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DOI: 10.1103/physreva.100.062117
Abstract: This work deals with quantum graphs, focusing on the transmission properties they engender. We first select two simple diamond graphs, and two hexagonal graphs in which the vertices are all of degree 3, and investigate… read more here.
Keywords: narrow peaks; full transmission; quantum graphs; graphs ... See more keywords
Nonuniversality in the spectral properties of time-reversal-invariant microwave networks and quantum graphs.
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DOI: 10.1103/physreve.95.052202
Abstract: We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide an ideal basis… read more here.
Keywords: long range; quantum graphs; time reversal; nonuniversality spectral ... See more keywords
Implications of Spectral Interlacing for Quantum Graphs
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DOI: 10.3390/e25010109
Abstract: Quantum graphs are ideally suited to studying the spectral statistics of chaotic systems. Depending on the boundary conditions at the vertices, there are Neumann and Dirichlet graphs. The latter ones correspond to totally disassembled graphs… read more here.
Keywords: spectral interlacing; quantum graphs; implications spectral; number ... See more keywords