Quantum graphs and dimensional crossover: the honeycomb

Quantum graphs and dimensional crossover: the honeycomb

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...

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Main Authors: Adami Riccardo, Dovetta Simone, Ruighi Alice
Format: Article
Language:English
Published: Sciendo 2019-01-01
Series:Communications in Applied and Industrial Mathematics
Subjects:
periodic graphs
nonlinear schrödinger
threshold phenomena
sobolev inequality
Online Access:https://doi.org/10.2478/caim-2019-0016
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spelling doaj-fc1b69ed7d784096905deae6a6b6d19d2021-09-06T19:22:00ZengSciendoCommunications in Applied and Industrial Mathematics2038-09092019-01-0110110912210.2478/caim-2019-0016caim-2019-0016Quantum graphs and dimensional crossover: the honeycombAdami Riccardo0Dovetta Simone1Ruighi Alice2Dipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129Torino, ItalyDipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129Torino, ItalyDipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129Torino, ItalyWe 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.https://doi.org/10.2478/caim-2019-0016periodic graphsnonlinear schrödingerthreshold phenomenasobolev inequality
collection DOAJ
language English
format Article
sources DOAJ
author Adami Riccardo
Dovetta Simone
Ruighi Alice
spellingShingle Adami Riccardo
Dovetta Simone
Ruighi Alice
Quantum graphs and dimensional crossover: the honeycomb
Communications in Applied and Industrial Mathematics
periodic graphs
nonlinear schrödinger
threshold phenomena
sobolev inequality
author_facet Adami Riccardo
Dovetta Simone
Ruighi Alice
author_sort Adami Riccardo
title Quantum graphs and dimensional crossover: the honeycomb
title_short Quantum graphs and dimensional crossover: the honeycomb
title_full Quantum graphs and dimensional crossover: the honeycomb
title_fullStr Quantum graphs and dimensional crossover: the honeycomb
title_full_unstemmed Quantum graphs and dimensional crossover: the honeycomb
title_sort quantum graphs and dimensional crossover: the honeycomb
publisher Sciendo
series Communications in Applied and Industrial Mathematics
issn 2038-0909
publishDate 2019-01-01
description 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.
topic periodic graphs
nonlinear schrödinger
threshold phenomena
sobolev inequality
url https://doi.org/10.2478/caim-2019-0016
work_keys_str_mv AT adamiriccardo quantumgraphsanddimensionalcrossoverthehoneycomb
AT dovettasimone quantumgraphsanddimensionalcrossoverthehoneycomb
AT ruighialice quantumgraphsanddimensionalcrossoverthehoneycomb
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