Quantum graphs and dimensional crossover: the honeycomb
Analysis of PDEs
2019-01-30 v1
Abstract
We summarize features and results on the problem of the existence of Ground States for the Nonlinear Schr\"odinger 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.
Cite
@article{arxiv.1901.10458,
title = {Quantum graphs and dimensional crossover: the honeycomb},
author = {Riccardo Adami and Simone Dovetta and Alice Ruighi},
journal= {arXiv preprint arXiv:1901.10458},
year = {2019}
}
Comments
Proceeding for the congress of the Italian Society of Applied and Industrial Mathematics (SIMAI) 2018, 17 pages, 6 figures