Spectra of periodic quantum graphs: some unusual features
Семинары
Совместный семинар отделов «Современная математическая физика» и «Математические проблемы теоретической физики»
Дата и время: четверг, 27 сентября 2018 г., в 14:30
Место: Конференц-зал им. Блохинцева (4-й этаж), Лаборатория теоретической физики им. Н.Н. Боголюбова
Тема семинара: «Spectra of periodic quantum graphs: some unusual features»
Докладчик: Павел Экснер (Институт математической физики и прикладной математики, Прага)
Аннотация:
Spectra of periodic quantum systems are usually expected to be absolutely continuous, consisting of bands and gaps, the number of the latter being determined by the dimensionality. Our aim is to show that if the systems in question are quantum graphs, some unusual spectral features may arise. Using simple examples, we show that the spectrum may then have a pure point or a fractal character, and also that it may have only a finite but nonzero number of open gaps. Furthermore, motivated by recent attempts to model the anomalous Hall effect, we investigate a class of vertex couplings that violate the time reversal invariance. We will find spectra of lattice graphs with the simplest coupling of this type, the one with `maximum’ non invariance, and demonstrate that it depends substantially on the lattice topology. Finally, we will discuss an interpolation between this «maximal» coupling and the usual Δ-type one.