We summarize features and results on the problem of the existence of Ground States for the Nonlinear Schrödinger Equation on doubly-periodic metric graphs. We extend the results known for the two-dimensional square grid graph to the honeycomb, made of infinitely-many identical hexagons. Specifically, we show how the coexistence between one-dimensional and two-dimensional scales in the graph structure leads to the emergence of threshold phenomena known as dimensional crossover.
Quantum graphs and dimensional crossover: The honeycomb / Adami, R.; Dovetta, S.; Ruighi, A.. - In: COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS. - ISSN 2038-0909. - 10:1(2019), pp. 109-122.
Titolo: | Quantum graphs and dimensional crossover: The honeycomb |
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Data di pubblicazione: | 2019 |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.2478/caim-2019-0016 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11583/2795496