<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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

Dipartimento di Scienze Matematiche “G.L. Lagrange”

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"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...

Quantum graphs and dimensional crossover: the honeycomb

Publié en ligne: 15 juin 2019

Pages: 109 - 122

Reçu: 30 janv. 2019

Accepté: 17 mai 2019

DOI: https://doi.org/10.2478/caim-2019-0016

Mots clés
periodic graphs, nonlinear Schrödinger, threshold phenomena, Sobolev inequality

© 2019 Riccardo Adami et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Quantum graphs and dimensional crossover: the honeycomb

Publié en ligne: 15 juin 2019

Pages: 109 - 122

Reçu: 30 janv. 2019

Accepté: 17 mai 2019

DOI: https://doi.org/10.2478/caim-2019-0016

Mots clésperiodic graphs, nonlinear Schrödinger, threshold phenomena, Sobolev inequality

© 2019 Riccardo Adami et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
periodic graphs, nonlinear Schrödinger, threshold phenomena, Sobolev inequality