International Laboratory "Mathematical Research Methods of Complex Physical Systems"

Full description of the spectrum of quantum graph with geometrical structure similar to branching grapheme nanoribbon (Figure 1) is given. Necessary and sufficient conditions for existence of bound states are obtained. The structure of the spectrum is shown in (Figure 2) (for positive potentials at the graph vertices (a) and for negative potentials (b)). The dependence of the spectral structure on the potential strength is characterized by Figure 3.

                                                                    

                                                                                            Figure 1

                                

                                                                                            Figure 2

                                                          

                                                                                                    Figure 3