Introduction to Quantum Graphs
By G. Berkolaiko, Peter Kuchment. 2012
1,016 citations recorded by the source corpus.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/439f26a0938b1c4617655d0f951eda77033aedbe
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Existence of infinite stationary solutions of the $L^2$-subcritical and critical NLSE on compact metric graphs (2017, background): “here a full topological characterization of the existence of ground states. Let us briefly recall some standard definitions and facts on compact metric graphs (for more details we refer for instance to [5, 14, 19]). Throughout the paper, a connected metric graph G = (V,E) denotes a connected metric sp”
- Boundary Value Problems, Weyl Functions, and Differential Operators (2020, methodology): “For boundary triplets and similar techniques in the analysis of quantum graphs see [110, 134, 172, 183, 196, 287, 289, 294, 536, 625, 637, 645, 646].”
- An overview of periodic elliptic operators (2015, methodology): “It has been implemented (as the so-called decoration procedure) in its simplest incarnations in the discrete situation [339], as well as in the quantum graph case [27, 246].”
- Dedalus: A flexible framework for numerical simulations with spectral methods (2019, background): “a network of connected segments with differential equations (see Berkolaiko and Kuchment [78] and Noja [79] for applications).”
- Surgery principles for the spectral analysis of quantum graphs (2018, result): “We will always assume the graph is compact, by which we mean that there is a finite number E = |E| of edges, each edge of finite length; this terminology is in keeping with [BK13].”
- NLS ground states on graphs (2014, background): “Here we present a rather informal description of the problem and of the main results of the paper, whereas a precise setting and formal definitions are given in Section 2, A metric graph G ([6, 12, 16]) is essentially a one-dimensional singular variety, made up of several, possibly unbounded interva”